Holographic printer

ABSTRACT

A holographic printer is disclosed which produces an intermediate hologram H 3  and uses the intermediate hologram H 3  to produce a white light viewable hologram H 2.

The present invention relates to a holographic printer.

Since the 1950s holograms have been produced by the technique ofilluminating a physical object with coherent light and arranging thatthe scattered light falls onto a photosensitive recording material thatis additionally illuminated by a mutually coherent reference beam (seefor example E. N. Leith et al., “Reconstructed Wavefronts andCommunication Theory”, Journal of the Optical Society of America 53,1377-81 1963). This basic technique suffers from the fact that aphysical object is required in order to produce the holographicrepresentation. Furthermore, the size of the holographic image mustusually correspond in a 1:1 fashion to the size of the physical objectbeing holographed. Such restrictions render this technique fundamentallyunsuitable for most practical applications. Another technique wherebythe fundamental interference pattern that characterizes a hologram iscalculated and then directly written onto a substrate is disclosed inU.S. Pat. No. 4,701,006). However the preferred-process of writing byelectron beam is costly and slow. In addition, for large holograms themagnitude of computation is usually prohibitive even with today'scomputational resources.

A technique for the generation of holograms not requiring an actualobject was proposed by King et al (Applied Optics, 1970). In this paperit was shown that holograms could be composed by optically multiplexinginformation taken from a plurality of perspective views consisting ofconventional 2-D photographs. In the case that such photographs weregenerated by computer no physical object was required at all (see forexample U.S. Pat. No. 3,843,225).

According to this approach, many conventional and sequential views of anobject are recorded by a camera mounted on a linear or circular track.Each of these views is then used in an optical system to multiplex thedata together so as to form an intermediate H1 hologram as described inU.S. Pat. No. 3,832,027. Such a hologram can then be converted ortransferred to a second hologram which is now white light viewable andis known as an H2 hologram. In order to do this, the H1 hologram isilluminated by laser light in a time-reversed geometry and the realimage so produced is used as the object for the H2 hologram. Uponillumination of this H2 hologram by a time-reversed reference beam awhite light viewable virtual image is reconstructed. Efficient andpractical commercial machines that convert H1 holograms to H2 hologramsnow exist (see for example M. V. Grichine, D. B. Ratcliffe, G. R.Skokov, “An Integrated Pulsed-Holography System for Mastering andTransferring onto AGFA or VR-P Emulsions” Proc. SPIE Vol. 3358, p.203-210, Sixth International Symposium on Display Holography, Tung H.Jeong; Ed.).

Holographic printing techniques which implicitly require the generationof an intermediate, or H1, hologram which is thereafter used to producea final white light viewable hologram are referred to as 2-stepholographic printing processes. The basic features of conventional2-step holographic printing are explained in U.S. Pat. No. 3,832,027.Subsequent work (e.g. Spierings W. et al., “Development of an OfficeHoloprinter II”, SPIE Vol. 1667 Practical Holography VI 1992) replacedthe photographic film used in U.S. Pat. No. 3,832,027 with an LCDscreen.

An elementary 2-step holographic printer, as described by Spierings etal., and based on U.S. Pat. No. 3,832,027, consists of an opticalvibration isolation table on which is mounted a traditional split-beamcontinuous-wave holography set-up. The object beam of this set-upilluminates a diffusion screen which is mounted parallel to, and whichis laterally displaced from, the photosensitive substrate onto which thehologram is to be recorded. A computer image is thus projected in laserlight onto the diffusion screen and the image is changed at each of aplurality of exposures. The photosensitive substrate is covered by aslit or rectangular aperture that is moved in a regular fashion witheach exposure, thus defining an effective holographic pixel of similarshape. A mutually coherent reference beam co-illuminates thisholographic pixel producing the required wave-interference on thephotosensitive substrate. Exposures are continued until all thephotosensitive substrate has been exposed sequentially by the aperture.The projected images are chosen to represent appropriate perspectiveviews of either real or computer generated objects from the viewpointdetermined by the position of the middle of the aperture slit(single-parallax case) or by the position of the middle of the rectangle(full-parallax case).

Due to the reliance of the above method on a continuous wave laser andthe intrinsic use of a diffusion screen onto which the image, in laserlight, is projected, the holographic printer is impractically bulky andexceedingly sensitive to vibration resulting in long write times. Theholographic printer is not therefore commercially viable.

An alternative scheme to a 2-step holographic printing process isdescribed in U.S. Pat. No. 4,206,965 whereby photographic images aredirectly multiplexed onto the final white light viewable hologram in theform of many long thin slit holograms located side by side, avoiding theneed for an intermediate H1 hologram.

All holographic printing schemes in which the final white light viewablehologram is printed directly without the need to generate anintermediate (H1) hologram are referred to hereinafter as 1-stepmethods.

U.S. Pat. No. 4,421,380 describes a system for producing 1-stepfull-colour transmission holograms from 3 interlaced strip or pointcomposite holograms of the achromatic type by the inclusion of aregistered colour-filter mask. U.S. Pat. No. 4,778,262 describes a1-step method for writing directly a two dimensional matrix of basicholograms from computer data. U.S. Pat. No. 5,138,471 describes asimilar technique wherein a one dimensional spatial light modulator isconnected to a computer to directly write (1-step) common types ofholograms as a two-dimensional matrix of basic holograms. U.S. Pat. No.4,834,476 describes another similar 1-step technique based oncomputational or sequential camera data whose use was described for thedirect writing of curved composite holograms having either a reflectionor transmission geometry but which technique could be generalized tomore conventional flat holograms.

U.S. Pat. No. 4,964,684 describes the use of a spatial light modulatorto help solve the problems of vibration in a real 2-step holographicprinter that produces an intermediate H1 hologram from computer orcamera data. U.S. Pat. No. 5,949,559 describes a method for directlywriting a holographic stereogram that has superior quality by cancelingoptical noise through the use of various moving diffuser screens.European application EP-0816952 describes a technique for realizinghigher quality composite holograms by using an imaged mask instead of areal mask. Japanese patent application JP-11084992 describes a vibrationisolation system for a holographic printing system that reduces theeffect of vibration and consequently improves hologram image quality.U.S. Pat. No. 5,973,807 describes the production of tiled holographicstereograms from camera or computer data via the intermediate step ofmultiple H1 holograms which are copied using a specific transfer processto form a larger composite display.

Yamagushi et al. (“Development of a prototype full-parallaxholoprinter”, Proc. Soc. Photo-Opt Instrum. Eng (SPIE) vol. 2406,Practical Holography IX, pp50-56 February 1995 and “High Qualityrecording of a full-parallax holographic stereogram with digitaldiffuser”, Optical Letters vol 19, no 2 pp 135-137 Jan. 20, 1994)describes a more advanced monochrome 1-step holographic printer based ona CW laser. The device was able to produce small full-parallaxwhite-light reflection holograms. However, it took 36 hours to writeeven a small hologram of 320×224 holopixels. In addition to onlyproducing monochrome holograms further disadvantages of the system arethat it can only produce holographic pixels of one size and it is unableto produce transmission type holograms. WO00/29909 (Klug et al.)overcomes some of the problems inherent with the system disclosed byYamagushi et al. This application describes a 1-step holographic printerthat is capable of producing 3-colour white light viewable full parallaxreflection holograms having a wide angle of view. This development is,however, still based on CW lasers and consequently suffers from veryslow printing speeds, a complex design and quality problems linked tovibrational interference.

In many cases a 2-step method of generating an intermediate H1 hologramfrom computer data and then copying or image-plane transferring thehologram to form a white light viewable hologram is to be preferred overthe method of directly writing the final hologram. This is due to anumber of reasons. It is frequently preferred to generate restrictedparallax holograms, having only horizontal parallax. With thetraditional 2-step technique that produces an intermediate H1 hologram,such an H1 hologram may essentially be composed of one or moreone-dimensional strips of overlapping holographic pixels. The classicaloptical transfer technique then takes care of the complex computationalstep of calculating the distribution of light over the entiretwo-dimensional surface of the final (H2) hologram. If such a finalhologram is written directly as in a 1-step printing scheme then thiscomputation must be done by computer. In addition, for large holograms,the time required to write a two dimensional array of holographic pixelsis usually proportional to the square of the time required to write atraditional H1 master hologram and as such can become prohibitively longfor some applications. A further problem with directly written 1-stepcomposite holograms is that they can appear pixelated whereas the 2-steptechnique of using an H1 master hologram is less prone to this problem.

Notwithstanding the above arguments, there are many applications whereit is advantageous to directly write the final hologram by a 1-stepscheme. Such directly written holograms require lower energy laserradiation than corresponding 2-step holographic printers. They are alsomore easily tiled together to form ultra-large displays. Also in manyapplications quick previews of the final hologram are required and itmay not convenient to produce an H1 hologram and then to put thishologram into another machine in order to generate the final H2hologram. The 1-step technique of directly writing holograms also allowsthe creation of hybrid holograms having non-standard viewing windows.,something that is likely be demanded by the printing industry in thecontext of holographic billboard displays. Further advantages of the1-step system are that materials such as photopolymers (see for exampleEuropean patent EP0697631B1) may be used which require only dryprocessing whereas the more sensitive Silver Halide materials requiringwet processing must be employed for classically copied traditional H2holograms due to simple energy considerations.

WO01/45943 and WO01/42861 describe a holographic printer based on amultiple colour pulsed laser system. The holographic printer is capableof producing either final 1-step H1 holograms or master H2 holograms forH2:H1 transfer. The holograms can either be reflection or transmissionholograms and they may have full or limited parallax. The holograms mayalso be monochrome, rainbow or full-colour. The printing speed of theholographic printer is several orders of magnitude faster than otherknown holographic printers. In addition, the holographic printer iscompact and the hologram quality is independent of externalenvironmental noise.

The known holographic printer disclosed in WO01/45943 and WO01/42861will now be described in more detail in relation to FIGS. 1-8. Forsimplicity and clarity the case of a single monochromatic laser will beconsidered although it should be understood that the this can beextended to a multiple colour laser system. FIG. 1 shows an overheadview of the holographic printer. A single colour single-frequency pulsedlaser 100 capable of rapid operation (typically 20 Hz) and havingsufficient temporal coherence emits a beam of coherent light that issplit by a variable beamsplitter 101. The beam 102 continues to themirror 103 whereupon it is diverted to the mirror 104 whereupon it isdiverted to the waveplate 105 that controls the polarization of thebeam. The beam continues to a telescope comprising lenses 106, 107 and167. Lens 107 is mounted on a motorized translation stage 108 with motor109. The diameter of the beam exiting from optic 107 is thus controlledand approximately collimated. The beam passes to a micro-lens array 110that expands it onto the collimating lens assembly 111. The distancebetween the elements 110 and 111 is chosen to be the effective focallength of the lens 111. In such a way a collimated beam exits the lens111 with a controllable spatial coherence. The beam now illuminates aliquid crystal display (LCD) 112, having a resolution 768×1024 pixelsand lateral dimension of 26.4 mm, which is mounted on a 2-D motorizedtranslation stage 116 having vertical control motor 115 and horizontalcontrol motor 118. Positions of maximum LCD horizontal displacement areindicated by 113 and 114. The LCD position is adjusted when writing H1type holograms and is used to attain a much higher resolution of thefinal image than would otherwise be possible with the same static LCDfor a given angle of view. The LCD position may also be adjusted whenwriting a 1-step hologram in order to maintain a particular hologramviewing window geometry.

After passing through the liquid crystal display, the beam traverses alinear polarizer that converts the LCD image from a polarizationrotation image into amplitude modulation. The beam then passes through awide-angle objective 119 mounted on the motorized translation stage 120with motor 163. This stage is used to control the position of thefocused image of the LCD produced by the objective 119. The size of theminimum waist 166 of the object beam is controlled by the motorizedstage 108 with motor 109. The object beam now comes to bear on thephotosensitive material 162 here shown as film mounted on a roll/stagesystem. The motor 129 controls movement of the stage 123 towards andaway from the position of minimum object beam waist. The rollers 124 and125 control the horizontal movement of the film 162 in front of theobject beam. The motor 128 controls the vertical movement of the film infront of said object beam. Motor 126 controls the motion of the rollers124 and 125. Rollers 122 and 131 tension the film and control thehorizontal angle that the film makes to the axial propagation vector ofthe object beam.

The reference beam is split from the main laser beam by the variablebeamsplitter 101 controlled by motor 165. The beam 135 is directed to amirror 136 whereupon it is reflected through an quasi-elliptical orrectangular aperture 137, an effective image of which is eventuallycreated at the intersection of the reference beam with the holographicrecording material, such quasi-elliptical or rectangular shape producinga defined circular or quasi-elliptical or rectangular referencefootprint on the recording material as may be required by the type ofhologram being written. The reference beam continues to the waveplate138 that controls the polarization of the laser beam. The elements 139and 141 with either 164 or 163 form a telescope that controls the sizeof the beam after 164/163 which is adjustable by the motorized stage 142with motor 143. The beamsplitter switch 144 either directs the referencebeam on the path 154 or onto the path 145. Path 145 is used to createtransmission holograms whereas path 154 is used to create reflectionholograms.

In the case of path 145 the reference beam passes through the lens 164that produces an approximate image of the aperture 137 at the recordingmaterial surface. This lens also corrects for the slight divergence ofthe light produced by the lens 141. The divergence of the light after164, which is ideally collimated, is thus controlled to withindiffraction limits. Practically this means that for small reference beamsize the beam will not be exactly collimated but that such departurefrom collimation will lead to an image blurring significantly less thanthat induced by the source size of the final hologram illuminationsource. Mirrors 146 and 149 now direct the reference beam onto itstarget to intersect the object beam at the surface of the holographicrecording material. Motorized rotation stages 147 and 150 with motors148 and 152 respectively and the linear translation stage 151 with motor153 ensure that different reference angles may be achieved for differentplacements and orientations of the recording material.

In the case of path 154 the reference beam passes through the lens 163that produces an approximate image of the aperture 137 at the recordingmaterial surface. This lens also corrects for the slight divergence ofthe light produced by the lens 141. The divergence of the light after163, which is ideally collimated, is thus controlled to withindiffraction limits as above. Mirrors 155 and 156 now direct thereference beam onto its target to intersect the object beam at thesurface of the holographic recording material, this time from theopposite side to the object beam. The motorized rotation stage withmotor 159 and the linear translation stage 158 with motor 160 ensurethat different reference angles may be achieved for different placementsand orientations of the recording material.

The holographic printer can function in a variety of different modes.FIG. 2 shows a diagram of the system in H1 transmission mode. Thereference beam comes in towards the recording material from the sameside as the object beam to form a holographic pixel 121. The holographicpixel 121 is significantly displaced from the point of minimum waist166. The image of the LCD 112 is located at a distance 201 from therecording material 162 and as such a screen placed at 202 would show asharply focused image of each 2-D picture loaded into the LCD 112. Theplane 202 usually corresponds to the H2 plane in a transfer geometry.

In order to record an H1 transmission hologram, perspective views of areal or computer generated object are pre-distorted to compensate forresidual optical distortion and for a certain final lighting geometry.Such images are then loaded into the LCD one by one, a holographic pixelis recorded, and then the recording material is advanced and the processrepeated for each image. For the case of the generation of a rainbowtransmission master hologram a line of pixels is written onto theholographic recording material as shown in FIG. 6(a). Each circlerepresents an interference pattern containing information about acertain perspective view along a horizontal viewing line. FIG. 6(b)illustrates the case pertaining to the generation of an RGB rainbowhologram master where three lines of pixels are written at theachromatic angle each line corresponding to a red, green or bluecomponent image in the axial viewing position of the final hologram. Therecording geometry for FIG. 6(b) is shown in FIG. 3.

In order to record an H1 transmission hologram suitable for thegeneration of a white light reflection hologram a grid a pixels havingdifferent vertical and horizontal packing densities is written as shownin FIG. 7. If a reflection type master hologram is required then thesystem is configured as shown in FIG. 4. In order to write a directone-step reflection hologram, the basic image data is mathematicallytransformed according to special pixel-swapping rules, with the systemconfigured as shown in FIG. 5, and pixels written as shown in FIG. 8.

Despite the various advantages provided by the known holographicprinter, many commercial applications require fundamentally higherspeeds of 1-step printing for medium to large-size RGB colour reflectionholograms. RGB holopixels at over 20 Hz in one-step mode can be recordedusing the holographic printer, but when sufficient resolution isdemanded, a 1 m×1 m hologram comprising 1 million RGB pixels will stilltake nearly 14 hours to print.

The known holographic printer can also produce H1 transmission hologramssuitable for the generation of RGB colour reflection holograms H2 byH1:H2 transfer. If the final hologram is to be of restricted parallax,which is frequently the case for larger prints, then the write time ofthe required master hologram(s) falls within acceptable limits. Forexample, a RGB master suitable for the production of a high-resolution 1m×1 m H2 hologram can be printed in around 30 minutes with thistechnique.

Despite this acceptable write-time, in order to produce a medium tolarge format H2 hologram of acceptable quality from a master or seriesof masters, a very high energy multiple-colour laser must be employed inthe H1:H2 transfer machine. This is because the quality of RGB colourreflection holograms is limited by Raleigh scattering of the bluecomponent which in turn is controlled by the grain-size of the recordingmaterial. In order to obtain acceptable Raleigh scattering in the blueit is necessary to use a smaller grain size than normally employed inconventional holography. This is turns leads to a rather lowersensitivity and hence to the requirement of large energies for the H1:H2transfer. Typically, for a 1 m×1 m H2 RGB hologram over 4 Joules isrequired in the blue component alone. Whilst possible to attain, such alaser is highly complex and costly.

Additionally, the fact that large collimated beams and a potentiallylarge distance between the H1 and H2 holograms are required during H1:H2transfer means that any commercial transfer machine would beparticularly bulky.

Thus, although the known holographic printer provides a significantimprovement over previous devices each 3D print ties up the holographicprinter for a long time if used in a 1-step operation and if used in a2-step operation the H1:H2 transfer equipment is both bulky andexpensive.

Accordingly, it is desired to provide an improved holographic printer.

According to the present invention there is provided a holographicprinter as claimed in claim 1.

The holographic printer according to the preferred embodiment comprisesone, two or more than two pulsed laser sources. One or more of thepulsed laser sources may produce a laser emission having a wavelength of946 nm, 1064 nm (or 1053 nm or 1047 nm or 1080 nm or 1070 nm), 1319 nm(or 1313 nm or 1338 nm or 1341 nm or 1351 nm) or in the range 1850-1970nm.

The laser emission may be frequency doubled to 473 nm, 532 nm (or 526 nmor 523.6 nm or 539.8 nm or 535 nm) or 659 nm (or 656.5 nm or 669 nm or670.7 nm or 675.5 nm), frequency tripled to 440 nm (or 437.7 nm or 446.0nm or 447.1 nm or 450.3 nm) or 617-657 nm or frequency quadrupled to awavelength in the range 463-493 nm.

Preferably, the pulsed laser source comprises a Nd:BEL, Nd:YAG, Nd:YAPor Nd:YLF laser source although in other embodiments a pulsed lasersource comprising Tm:YAG, Tm:YAL or Thulium in a host matrix ofPotassium Yttrium Ytterbium Tungstate may be used.

At least one pulsed laser source is preferably configured to producelaser emissions of single longitudinal mode and may be configured toproduce laser emissions having a temporal coherence length greater than1 mm. At least one pulsed laser source may comprise a means formodifying the laser emission wavelength by Raman scattering or Ramanamplification.

According to a less preferred embodiment, one or more CW laser sourcesmay be used. Preferred CW laser sources include HeNe, Krypton, Argon,Neodymium, dye and HeCd.

Preferably, red and/or green and/or blue laser beams are generated forwriting holograms. The red laser beam preferably has a wavelength in therange 615-680 nm, the green laser beam preferably has a wavelength inthe range 510-550 nm and the blue laser beam preferably has a wavelengthin the range 430-480 nm.

According to a particularly preferred embodiment the final white lightviewable hologram may be an RGB white light viewable reflectionhologram.

The holographic printer preferably comprises one or more spatial lightmodulators onto which digital data is displayed for laser-writing ontoan intermediate hologram. The digital data may be derived from a realmodel or from a 3-D computer model. The digital data may bemathematically transformed to correct for optical distortion.

The optical distortion which is corrected may be selected from the groupconsisting of: (i) H2 emulsion swelling on hologram processing; (ii)reference beam angle errors; (iii) finite emulsion refractive index andemulsion refractive index not equalling recording material substraterefractive index; (iv) required H2 replay wavelength not equallingrecording wavelength; (v) required H2 replay reference angle notequalling recording reference angle; and (vi) intrinsic opticaldistortion of the printer including distortion due to the principleobjective(s).

Preferably, the digital data is mathematically transformed by a singlesimple pixel swap that operates between an initial image data set and adata set displayed on said one or more spatial light modulators.

Preferably, the digital data is mathematically transformed by a seriesof simple pixel swaps.

According to the preferred embodiment the one or more intermediateholograms (the “H3” hologram(s)) are transmission holograms. The one ormore intermediate holograms are formed on a first substrate which maycomprise a photosensitive medium, a thermoplastic substrate, aphotopolymer substrate or a silver halide emulsion coated substrate.

Preferably the digital data written onto the H3 intermediate hologram(s)is calculated by special transformation of the camera data set and isthus generally different from the digital data that would normally bewritten onto an H1-type hologram (i.e. untransformed camera data).

According to a less preferred embodiment, the one or more intermediateholograms are reflection holograms which are preferably written on aphotosensitive medium.

Preferably, the holographic printer further comprises positioning meansfor positioning the first substrate so that a holographic pixel iswritten on the first substrate. The positioning means moves the firstsubstrate so that an array of holographic pixels is formed thereon.

Different colour holographic pixels may be recorded at the same positionon the first substrate so that different colour holographic pixelsoverlap one another. Alternatively, different colour holographic pixelsmay be recorded at different positions on the first substrate so thatdifferent colour holographic pixels do not substantially overlap oneanother.

Preferably, in the second mode the output from the pulsed laser sourcesis amplified.

In the second mode a first order diffracted beam may be produced at theintermediate hologram from a selected group of pixels. A secondsubstrate on to which the white light viewable hologram (the “H2”hologram) is to be written is preferably positioned parallel to thefirst substrate.

Preferably, the second substrate is positioned at a distance d from thefirst substrate wherein d is greater than zero and less than thedistance between the camera (H1) plane and the H2 plane.

Preferably, the second substrate is positioned at a distance d from thefirst substrate wherein d is greater than zero and less than ¼ of theheight of the one or more intermediate holograms.

Preferably, the second substrate is positioned at a distance d from thefirst substrate wherein d is greater than zero and less than ¼ of thewidth of the one or more intermediate holograms.

A mask may be arranged adjacent the second substrate so that a portionof the diffracted beam illuminates the second substrate (defining a“super pixel” on the H2). A zeroth order diffracted beam is preferablysubstantially prevented from illuminating the second substrate.

One or more line-pass optical filters may be placed between the firstsubstrate and the second substrate and the one or more line-pass opticalfilters may comprise an interference filter.

Super-pixels comprising superimposed red, green and blue holographicpixels are preferably written on to the second substrate. Thesuper-pixels may or may not substantially overlap.

The white light viewable hologram (H2) is preferably a reflectionhologram.

According to a second aspect of the present invention there is provideda hologram produced by a 2-step holographic printer.

Preferably, the hologram is a single parallax hologram. Alternatively,the hologram is a full parallax hologram.

According to a third aspect of the present invention, there is provideda method of printing a hologram as claimed in claim 50.

The preferred embodiment represents a significant improvement over theknown holographic printer. The known 2-step method requires a largepulsed laser for generating large format RGB white-light reflectionholograms. Similarly, the 1-step method requires too long a time towrite a large format RGB white-light reflection hologram. The preferredembodiment overcomes these problems by providing a 2-step printer thatis capable of producing multiple holograms in a reasonable time frameusing only a small laser.

Another advantage of the preferred embodiment over other methods ofrapid copy generation (such as the contact copy method proposed inWO00/29908) is that, at H3:H2 transfer, the ratio of the H3 illuminationbeam energy to the H2 reference beam energy can be adjusted for eachcolour channel. This allows a higher quality copy to be generated andallows the proper balance of colours on different emulsions without theneed for reprinting.

The preferred embodiment also allows the production of holograms thatare designed for illumination by a point source, rather than by acollimated reference beam.

The preferred embodiment produces holograms in which the standardpixelisation observed with the known holographic printer is reduced dueto the finite distance between the H3 and H2 planes.

The use of a thermoplastic emulsion for the H3 hologram is particularlyadvantageous in that it avoids much of the inconvenience associated withthe known 2-step method.

The preferred embodiment contains a single low-energy multiple-colourpulsed laser. Instead of producing either a 1-step hologram or aconventional H1 (master) hologram the preferred embodiment produces adifferent type of intermediate hologram known as an H3 hologram fromwhich the same holographic printer can then generate a final RGBwhite-light viewable H2 reflection hologram. The time required for thegeneration of the H3 hologram is shorter than the known 1-step H1hologram generation time. Furthermore, the time required to generate afinal H2 colour hologram from the H3 hologram is several orders ofmagnitude faster than the using a 1-step approach.

The preferred embodiment provides a compact, rugged and relativelysimple holographic printer capable of producing multiple high-qualityfull-colour digital full-parallax reflection holograms of flexibleformat and on a timescale suited for commercial applications.

The preferred embodiment also provides a single method and apparatus forproducing colour or monochromatic reflection holograms from digitaldata. Such holograms may either be of restricted parallax orfull-parallax. In one embodiment the data is generated entirely by acomputer as a 3-D (animated) model. In another embodiment the data isgenerated from multiple 2-D camera images taken of a real 3-D object orscene from a plurality of different camera positions. The data isdigitally processed and the various chromatic components are displayedon small high-resolution spatial light modulators that are illuminatedby laser radiation.

In a preferred embodiment a compact low-energy pulsed laser systemcapable of generating emissions at two or more chromatic components isused to record a composite transmission intermediate hologram on apanchromatic holographic emulsion. This intermediate hologram isreferred to as an H3 rather than an H1 hologram as the digital datarecorded onto it do not correspond to the data recorded onto atraditional Hi hologram.

After recording, the H3 master hologram is chemically processed, driedand reloaded into the holographic printer. The same pulsed laser,operating preferably at a higher energy is then used to illuminatesuccessively, at angles identical to the recording angles, sequentialand overlapping small zones of the H3 intermediate hologram, the areaseach containing a plurality of recorded H3 holographic pixels. The firstorder diffracted radiation from each such exposure is then used toexpose a plurality of small holograms onto another panchromaticphotosensitive plate (the H2 hologram) that is held parallel andlaterally displaced to the H3 hologram. The H2 hologram maintains at alltimes a fixed and static geometrical relationship to the H3 hologram andthe ensemble of H2 and H3 is usually moved whilst the laser remainsstatic. The size of each recorded H2 sub-hologram is determined by astatic mask in close proximity to the (moving) H2 hologram and by thesize of a co-illuminating but oppositely directed reference beam that isbrought to bear onto the H2. In conventional H1:H2 transfer the distancebetween the H1 hologram and the H2 hologram during transfer correspondsto the final optimal viewing distance of the H2 (typically >50 cm) andalso to the distance from the H2 to the camera plane. In H3:H2 transferthe H3 is placed much closer to the H2 and neither the final optimumviewing distance of the H2 nor the H2 to camera-plane distancecorresponds to this separation. The preferred embodiment thus provides amethod whereby an H3 hologram can be very rapidly transferred to an H2hologram by the same machine that writes the H3 without the need for thehigh energies required by conventional H1:H2 transfer.

According to a fourth aspect of the present invention, there is provideda 2-step holographic printer as claimed in claim 51.

According to a fifth aspect of the present invention, there is provideda 2-step holographic printer as claimed in claim 52.

Preferably, the data ^(μν)S_(αβ) is subsequently treated for opticaldistortions inherent in the writing system and in the viewing geometryof the H2.

Preferably, the data transformations for ^(μν)S_(αβ) are modified so asto take into account the optical distortions inherent in the writingsystem and in the viewing geometry of the H2.

Preferably, the terms: $\begin{matrix}{{u = {\left( {\mu - 1} \right)\frac{\Pi}{\left( {N_{M} - 1} \right)}}},} & {{\mu = 1},\ldots\quad,N_{M}} \\{{v = {\left( {\upsilon - 1} \right)\frac{\Sigma}{\left( {N_{V} - 1} \right)}}},} & {{\upsilon = 1},\ldots\quad,N_{V}}\end{matrix}$are substituted by: $\begin{matrix}{u = {\frac{\Pi}{2} + {\left\lbrack {{\left( {\mu - 1} \right)\frac{\Pi}{\left( {N_{M} - 1} \right)}} - \frac{\Pi}{2}} \right\rbrack\psi_{\mu\quad v}}}} & {{\mu = 1},\ldots\quad,N_{M}} \\{v = {\frac{\Sigma}{2} + {\left\lbrack {{\left( {v - 1} \right)\frac{\Sigma}{\left( {N_{V} - 1} \right)}} - \frac{\Sigma}{2}} \right\rbrack\psi_{\mu\quad v}}}} & {{\upsilon = 1},\ldots\quad,N_{V}}\end{matrix}$wherein ψ_(μv) is a function describing optical distortion inherent inthe system.

According to a sixth aspect of the present invention, there is provideda holographic copying device as claimed in claim 55.

Preferably, the one or more intermediate holograms (H3) are written on afirst substrate and the white light viewable hologram (H2) is to bewritten on a second substrate.

Preferably, the second substrate on which the white light viewablehologram (H2) is to be written is positioned parallel to the firstsubstrate.

Preferably, the second substrate is positioned at a distance d from thefirst substrate wherein d is greater than zero and less than thedistance between the camera (H1) plane and the H2 plane.

Preferably, the second substrate is positioned at a distance d from thefirst substrate wherein d is greater than zero and less than ¼ of theheight of the one or more intermediate holograms.

Preferably, the second substrate is positioned at a distance d from thefirst substrate wherein d is greater than zero and less than ¼ of thewidth of the one or more intermediate holograms.

Various embodiments of the present invention together with otherarrangements given for illustrative purposes only will now be described,by way of example only, and with reference to the accompanying drawingsin which:

FIG. 1 shows a plan view of a known holographic printer;

FIG. 2 shows the known holographic printer working in an H1 masterhologram writing mode for the case of a transmission H1 hologram;

FIG. 3 shows the known holographic printer working in an H1 masterhologram writing mode for the case that the holographic recordingmaterial is orientated at the achromatic angle;

FIG. 4 shows the known holographic printer working in an H1 masterhologram writing mode for the case of a reflection H1 hologram;

FIG. 5 shows the known holographic printer working in a direct (or1-step) writing mode for the case of a reflection hologram;

FIG. 6(a) shows for the case of the known holographic printer theoverlapping object beam density pattern recorded on the holographicmaterial typical of an H1 master hologram written for the creation of arainbow hologram by conventional transfer with each circle containingthe perspective information for a certain viewpoint and FIG. 6(b) showsfor the case of the known holographic printer the overlapping objectbeam density pattern recorded on the holographic material typical of anH1 master hologram written for the creation of a full-colour rainbowhologram by conventional transfer with each ellipse containing theperspective information for a certain viewpoint, the three rowsrepresenting the three primary colour separations;

FIG. 7 shows for the case of the known holographic printer theoverlapping object beam density pattern recorded on the holographicmaterial typical of an H1 full aperture master hologram written for thecreation of a mono or full colour reflection hologram by conventionaltransfer with each circle containing the perspective information from acertain point in space as shown in FIG. 9;

FIG. 8 shows for the case of the known holographic printer the objectbeam density pattern recorded on the holographic material typical of adirectly written (1-step) hologram with each circle containing thedirectional and amplitude information of light originating from thatpoint that constitutes the 3-D image;

FIG. 9 shows the process of acquiring data from a series of sequentialcamera shots that can be used to generate the holograms and alsorepresents a computer model of an object where a viewing plane isdefined on which perspective views are generated;

FIG. 10 shows the mathematical discretization of the camera trackingplane and the hologram plane;

FIG. 11 shows the mathematical discretization of the camera photo frameand the H3 hologram plane;

FIG. 12 shows a plan view of a preferred embodiment (H3 shown here fromside);

FIG. 13(a) shows overhead and side views of the H3 hologram illustratingvarious reference beam geometries used for the writing of said H3hologram wherein identical azimuthal and altitudinal angles of referenceare used, FIG. 13(b) shows corresponding views where differingaltitudinal angles but identical azimuthal angles are used and FIG.13(c) shows corresponding views where widely differing azimuthal anglesare used;

FIG. 14 shows a section through the H3 and H2 planes viewed from theside during H3:H2 transfer showing how individual H2 super-pixels arebuilt up and overlapped;

FIG. 15 shows an overhead view of the H2 (1501), H3 (1502) andcamera/viewing planes (1503) for the case of a viewing window of thesame horizontal dimensions as the H2 hologram;

FIG. 16 shows a side view of the H2 (1501), H3 (1502) and camera/viewingplanes (1503) for the case of LCD aspect ratio equaling the H2 aspectratio and for the case of a viewing window of the same vertical andhorizontal dimensions as the H2 hologram;

FIG. 17 shows a side view of the H2 (1501), H3 (1502) and camera/viewingplanes (1503) for the case of a viewing window of the same vertical andhorizontal dimensions as the H2 hologram and for the general case of theLCD aspect ratio not equaling the H2 aspect ratio;

FIG. 18(a) shows an overhead view of the H2 (1501), H3 (1502) andcamera/viewing planes (1503) for the case of a general sized viewingwindow and FIG. 18(b) shows an overhead view of the H2 (1501), H3 (1502)and camera/viewing planes (1503) for the case of a general sized viewingwindow and an alternative H3 geometry;

FIG. 19(a) shows a side view of the H2 (1501), H3 (1502) andcamera/viewing planes (1503) for the case of a general sized viewingwindow and FIG. 19(b) shows an side view of the H2 (1501), H3 (1502) andcamera/viewing planes (1503) for the case of a general sized viewingwindow and an alternative H3 geometry; and

FIG. 20 shows the normalized object and image planes of a hologramwriting objective having finite distortion.

A preferred embodiment will now be described in more detail and withreference to FIG. 12 which shows a plan view of a preferred holographicprinter. The device has two basic modes of operation. The first modeallows the recording of an H3 intermediate (or master) hologram fromdigital data. The second mode allows the transfer of this H3 hologram toa conventional H2 hologram. The multiple colour pulsed laser used inthis embodiment is described in more detail in WO02/29487.

H3 Generation Mode

A Neodymium YAG ring oscillator 1201 is used to generate a train ofsingle frequency 50 ns laser pulses at 1064 nm in TEM00 mode at around20 Hz. When functioning in H3 generation mode the automated beamsplitterswitch 1203 is used to switch the radiation produced by 1201 directlyinto the element 1225. In H3:H2 transfer mode the switch 1203 transfersthe radiation produced in 1201 into element 1205.

The radiation at 1064 nm is now converted to 532 nm by the harmonicdoubling element 1225. Thereafter the variable automated attenuator 1226is used to control the energy of the radiation. The automated variablebeamsplitter 1227 is now used to split the radiation at 532 nm into anobject and reference beam. The reference path comprises an automatedvariable telescope 1229 (incorporating automated aperture 1228 forreference-beam footprint control), compensating lens 1230 and transfermirrors 1231 and 1232. These elements allow the size and shape of thereference beam at the position 1233 to be controlled and matched to thesize and shape of the object beam.

The 532 nm object beam is formed initially by the variable automatedbeam expander/collimator 1234 and iris 1235. Thereafter the collimatedbeam, now of a variably controlled size, illuminates a microlens array1236. The expanded radiation is then recollimated by the lens 1237(whose focal length is chosen to be equal to the distance between theelements 1236 and 1237) before illuminating the Liquid crystal displayunit (LCD) 1238 onto which specially transformed digital data isdisplayed.

The radiation transmitted by the LCD 1238 passes through a polarizer1239 in order to transform the digital data into an amplitude modulationof the LCD illuminating radiation. The radiation is thereafter passedthrough a wide-angle objective 1240. The object beam is then finallybrought to an approximate focus at the position 1233 on thephotosensitive material, coincident with the reference beam and whereinterference between the object and reference beams creates a greenholographic pixel.

The photosensitive medium 1219 is moved in a plane normal to thepropagation vector of the axial ray of the object beam in such a way asto record neighbouring green pixels evenly (or unevenly) over a2-dimensional grid. As mentioned above, the laser oscillator flashes ataround 20 Hz. At each flash a green pixel is thus written and thematerial 1219 is then advanced in one direction by a fixed amount. Thedigital data feeding the green LCD 1238 is then updated and anothergreen pixel is written. When one line of pixels has been terminated thephotosensitive material is moved in a direction orthogonal to theprevious linear motion and another line of green pixels is commencedparallel to the previous line. This process continues until a2-dimensional area of the material 1219 has been covered withholographic pixels.

Since the material 1219 can have significant inertia and further sincethe pulse repetition rate of the laser oscillator is relatively high thematerial 1219 is moved electromechanically either at a constant velocity(case of evenly spaced pixels) or using a programmed velocity curve(case of changing space between pixels). In both cases the laser flashand LCD update are synchronized to the photosensitive material positionand errors corrected by continual adjustment of the laser flash rate.

Single frequency TEM00 50 ns red and blue laser pulses are generatedrespectively by doubling and tripling of fundamental radiation at 1319nm produced by the ring Neodymium YAG laser oscillator 1202. Thisoscillator works at 20 Hz and is synchronized to 1201. When functioningin H3 generation mode the automated beamsplitter switch 1204 is used toswitch the radiation produced by 1202 directly into the element 1253. InH3:H2 transfer mode the switch 1204 transfers the radiation produced in1201 into element 1241.

Element 1253 converts radiation at 1319 nm into harmonically doubledradiation at 659 nm and further transmits a part of the 1319 nm to thetripling unit 1254 which in turn produces radiation at 440 nm. The redand blue channels are now treated in exactly the same way as describedin relation to the green channel.

Thus the variable automated attenuator 1255 is used to control theenergy of the blue radiation. The automated variable beamsplitter 1256is now used to split the radiation at 440 nm into an object andreference beam. The reference path comprises an automated variabletelescope 1258 (incorporating automated aperture 1257 for reference-beamfootprint control), compensating lens 1259 and transfer mirrors 1260 and1261. These elements allow the size and shape of the reference beam atthe position 1262 to be controlled and matched to the size and shape ofthe object beam.

The 440 nm object beam is formed initially by the variable automatedbeam expander/collimator 1263 and iris 1264. Thereafter the collimatedbeam, now of a variably controlled size, illuminates a microlens array1265. The expanded radiation is then recollimated by the lens 1266(whose focal length is chosen to be equal to the distance between theelements 1265 and 1266) before illuminating the LCD 1267 onto whichspecially transformed digital data for the blue channel is displayed.

The radiation transmitted by the LCD 1267 passes through a polarizer1268 in order to transform the blue digital data into an amplitudemodulation of the blue LCD illuminating radiation. The radiation isthereafter passed through an objective 1269 that is described in moredetail in WO01/45943 (modified here for operation at 440 nm). The blueobject beam is then finally brought to an approximate focus at theposition 1262 on the photosensitive material, coincident with the bluereference beam and where interference between these object and referencebeams creates a blue holographic pixel.

The red object and reference beams are formed in a manner identical tothe blue and green beams. For clarity purposes only the red referencebeam circuit has been omitted from FIG. 12.

Preferably, the distance between the red, green and blue pixel writinglocations (1308 & 1309 in FIG. 13) is an integer multiple of theincremental photosensitive material advance distance between flashessuch that different colour pixels can either (i) be precisely overlappedor (ii) remain strictly adjacent to partner colours.

The H3 hologram is a panchromatic composite transmission hologram. Inone embodiment (FIG. 13(a)) each colour channel is recorded (using arelatively thin emulsion layer) at the same altitudinal (approxBrewster's angle) and azimuthal (±180°) reference beam angles. A sectionof the H3 holographic plate (1302) is shown from above on the left-handside of the diagram and from the side on the right-hand side of thediagram. Green (1301), Red (1303) and Blue (1304) holographic pixels arewritten using the reference beams 1305, 1306 and 1307 which all make thealtitudinal angle 1310 to the H3 plane.

In another embodiment (FIG. 13(b)) each colour channel is recorded(using a rather thicker emulsion layer) at somewhat differentaltitudinal angles but at the same azimuthal (±180°) reference beamangle.

Less preferably, in yet another embodiment the azimuthal angles of eachchromatic reference beam are chosen to be widely separated (FIG. 13(c)).

Note that FIG. 12 illustrates the first alternative discussed abovewhere identical altitudinal and azimuthal (±180°) angles of referencefor the green and blue channels are shown. The red channel reference isnot shown for reasons of diagrammatic clarity but would mimic either theblue or green. The distances 1308 and 1309 in FIG. 13 are preferablychosen to be the same although according to less preferred embodimentsthey could be different. Holographic pixels 1301, 1303 and 1304 arepreferably arranged to be in a straight line but less preferredembodiments are contemplated wherein they are not arranged in a straightline.

H3:H2 Transfer Mode

This mode is used to write a conventional H2 hologram using anintermediate H3 hologram. The H3 hologram is written as described aboveand subsequently processed either chemically, thermally or opticallydepending on the particular photosensitive material used. The completedH3 hologram 1219 is then replaced in its original position in thedevice.

The laser oscillators 1201 and 1202 function as in the H3 generationmode (20 Hz synchronized operation). However, in the H3:H2 transfer modethe electromechanical beam switches 1203 and 1204 switch the radiationat 1053 nm and 1313 nm to respective amplifier units, 1205 and 1241.These amplifier units take the small energies produced by the laseroscillators 1201 and 1202 (typically around 10-15 mJ) and convert thisinto an emission of around 5 to 10 times higher which is thenharmonically converted by the units 1242 and 1206 into respectivelyemissions in the red (659 nm) and blue (440 nm) and an emission in thegreen (532 nm). For clarity, as in the case of the H3 generation modethe red channel (1243) is not shown in FIG. 12 as this channel issimilar to the blue and green channels. Since each colour channelfunctions similarly, only the green channel will be described in detail.

The green laser radiation produced by the harmonic converter 1206 isdirected by the transfer mirror 1207 to an electromechanicallycontrolled beamsplitter and/or attenuator unit 1208. This optical unitis used to split the beam into an object and reference of controllableratio and total energy. Elements 1210 and 1214 are λ/2 waveplates thatare used to adjust the polarization of both object and reference to therequired matched values to ensure both maximum interference and alsominimum parasitic reflection from the H3 1219 and the H2 1220. Thereference beam is thus transferred by mirror 1209 to mirror 1213, thepolarization is then adjusted at 1214 before being transferred again bymirror 1215 to the electromechanically controllable collimator and beamexpander unit 1216. This unit is used to control the diameter (and inmore advanced applications the footprint shape) of the collimated beam1223 incident on the photosensitive material 1220.

The object beam polarization is adjusted as previously described byelement 1210 after which the beam is directed via mirror 1211 to theelectromechanically controllable collimator and beam expander unit 1212.This unit is used to control the diameter (and in more advancedapplications the footprint shape) of the collimated beam 1217 thatilluminates the H3 1219.

The azimuthal and altitudinal angles of the green reference replay beam1217 are chosen to match exactly those used at recording. In this waythe beam 1217 produces a first order diffracted beam at the zone ofillumination of 1219 that faithfully reproduces the original object beamrecorded on the H3 at this location. A mask 1221 fixed in very closeproximity to the recording material 1220 is used to select a definedportion of the diffracted radiation (delineated by 1222 and 1223) by theaperture 1224 which is located centrally with respect to the illuminatedzone of the H3. The shape and size of this aperture is matched (eithermanually or electromechanically or electro-optically) to the shape andsize of the reference beam 1223. In this way a macroscopic section ofthe green channel of the H2 hologram is written at the zone 1224 at eachlaser flash.

Since the green object radiation illuminates not only the hologramoriginally written by the green master channel but also the hologramswritten by the red and blue channels it is necessary to suppress theparasitic diffraction due to the other two channels. In the embodimentof FIG. 13(a) this is done by installing a small line-pass interferencefilter at 1224. In the embodiment of FIG. 13(b) this is doneautomatically by the Bragg selection properties of the thicker emulsionlayer that is used in this case. In the embodiment of FIG. 13(c) widelydiffering azimuthal angles are used to ensure that the parasiticradiation falls outside the zone delineated by 1224. Finally, it is alsopossible to ensure the absence of parasitic diffraction at 1224 bychoosing to record three separate H3 holograms and transferring eachhologram, one at a time, to the final panchromatic H2.

By changing the size of the reference beam 1216 and the aperture 1224larger or smaller sections of the H2 can be written in parallel.However, the zeroth order diffracted beam 1218 produced by the H3 mustnot illuminate the photosensitive material 1220. The angles of the lines1222 and 1223 determine the final viewing angle range of the H2hologram. Thus effectively, for a given H3:H2 distance, the altitudinalH3 recording angle determines the maximum practical size of the H2section that can be written at each flash for a given H2:H3 distance.The consideration of parasitic reflection from the H3 both on recordingand replay usually constrains the choice of altitudinal angle to aroundthe Brewster's angle.

During writing, both the H2 hologram 1220 and the H3 hologram 1219 aremoved electromechanically together while the mask 1221 is keptstationary as indicated by the arrows in FIG. 12 (the movement is alsoout of the paper in FIG. 12 as well as in the horizontal direction). Ateach laser flash adjacent macroscopic zones 1224 of the H2 are recorded.These zones may be strictly adjacent or may be overlapped somewhat inorder to remove any grid-like effect on the final hologram.

Both the red and blue channels of the device function identically to thegreen channel here described. The zone 1252 (with optional line-passinterference filter) locates the blue H2 writing zone. The red writingzone is not shown. The distances between the various writing zones thatcorrespond to the different colour channels should be chosen carefullyso the different colour writing zones fall exactly on top of each otherin the final hologram. If this is not done discolouration problems maybe observed. This is illustrated in FIG. 14 which shows a slice throughthe H3 (1404) and H2 (1405) viewed from the side. Reference beams(green-1401, red-1402 and blue-1403) illuminate the zones 1406, 1407 and1408 on the H3. Aperture mask 1405, corresponding to 1221 of FIG. 12,defines the H2 green (1410), red (1411) and blue (1412) writing zones.These zones will be referred to hereinafter as super-pixels as they arethe holographic pixels of the H2 but are themselves composed of many H3pixels which are out of the H2 plane and so are somewhat defocused. Theholographic H2 substrate 1409 is shown grossly thicker than in realityin order to indicate the relative position of H2 super-pixels clearly.At the first laser flash just three super-pixels are written (1410, 1411and 1412). Before the next laser flash the H2 and H3 are advanced by adistance 1422 and an extra three super-pixels are written as shown onthe displaced H2 1414. After the third flash the H2 looks like 1415 andafter a number of flashes the H2 looks like 1416. Note that regions 1417and 1418 now show the different colour super-pixels beginning tooverlap. 1426 shows a final portion of the H2 where all three colourshave completely overlapped. Thus 1423, 1425 and 1424 are each composedof green, red and blue exactly-superimposed super-pixels.

In order to ensure exact overlap of different colour H2 super-pixels thedistances 1420 and 1421 are both exactly divisible by the H2/H3 advancedistance 1422. If the super-pixel width 1419 corresponds to the H2/H3incremental advance distance 1422 (as in fact shown in FIG. 14) then allpixels of one colour sit exactly side by side without overlap. However,some super-pixel overlap can be advantageous and thus the distance 1422may be chosen to be a little smaller than 1417.

All the reference beams (FIG. 12—green 1223, blue 1275, red not shown)are carefully adjusted to have exactly the same altitudinal andazimuthal angles of incidence. The angle of azimuthal incidence shouldusually be chosen such that the final hologram may be viewed by anoverhead light as would normally be required. Slight differences in theangles of incidence between the various colours leads tonon-registration of the various chromatic images in the H2 hologram.

Typically, the H3 hologram is written with holographic pixels of 2 mmdiameter. The different colour components are made to overlap perfectlyso that red, green and blue pixels are always printed one on top of theother. The form of the H3 holographic pixel is quasi-rectangular so onlya little overlapping is required to attain full and even coverage of theH3 substrate. Preferably, the Fourier plane of each object beamcoincides with the H3 substrate plane although some offset distance canbe used if required. Typical H3 hologram sizes produced by theembodiment of FIG. 12 vary from 30×40 cm to 1 m×1 m. Larger sizes may begenerated by simply changing the electromechanical advancementmechanisms of the device. Since the H3 is preferably a transmission typeof hologram it is possible to use a panchromatic fine-grain recordingmaterial (grain size ˜40 nm) for writing the H3 without problem. Thisallows very low energies to be used for writing the H3 and also helpsconsiderably when the H3 is transferred to an H2 hologram. To write anH3 hologram appropriate for transfer to a 1 m×1 m H2 takes around 200minutes.

In the H3:H2 transfer mode, for each colour channel, typically around1000 pixels on the H3 (˜40 cm²) are illuminated (by beams 1217 and 1272and not shown for red). The write size at each laser flash on the H2 isaround 4 cm² (e.g. 1224, 1252 and not shown for red) or around 10 timessmaller. This allows an H2 hologram of 1 m×1 m to be written in around 2minutes.

Since the H2 hologram is a reflection hologram a standard fine-grainemulsion (grain size ˜40 nm) cannot be used effectively as Raleighscattering in the blue channel is too great. Therefore, a panchromaticemulsion having a grain size of around 25 nm is preferably used.Although this material has a rather lower sensitivity than a normal finegrain emulsion (e.g. around 1 mJ/cm² in the green) the fact that thewriting zone on the H2 is usually around 10 times smaller than theillumination area on the H3 means that the energy required in the H2reference is of the same order of magnitude as that required by the H3illumination beam. Typically in the green around 2 mJ is required towrite the H3 and around 15 mJ to write the H2 (of which 75% is requiredfor illumination of the H3). Figures are similar for the red and bluecomponents.

3-D Data

As described above, an H3 is produced from transformed 3-D digital datathat are displayed on various LCDs within the device. How this 3-D datais defined, transformed and used will now be described.

In one embodiment a computer is used to generate a three dimensionalmodel of an object using a standard commercial computer program. Suchcomputer programs can produce very lifelike models using a variety ofsophisticated rendering processes that mimic real life effects. Inaddition advances in computer technology have now seen the calculationtimes, required for such programs to run, dramatically decreased. Threedimensional scanners using Moire or other principles now permit theincorporation of real world 3-D images in such computer models. Thestorage memory required for such 3-D models is largely dependent on thetexture maps used therein and hence computer files representing such 3-Dmodels are usually relatively small and may be transmitted over theinternet easily. In the preferred embodiment such 3-D computer modelsare used to generate a series of 2-D camera views from a virtual viewingplane as shown in FIG. 9. Here the viewing plane is labeled 901 andindividual 2-D perspective camera images, such as 905 and 904, of thecomputer represented object 1100 are generated at multiple locations onthe viewing plane such as 902 and 903. The spacing and density of such2-D views are generally controlled according to the information requiredfor a certain type of hologram but in one embodiment they form a regular2-D matrix and in another a regular horizontal 1-D array. In anotherembodiment a real model is used instead of a computer representation anda real camera is employed to record individual photographs (eitherdigitally or via photographic film that is subsequently digitized). Insuch a case FIG. 9 should be interpreted in the following fashion.Object 900 represents the object to be holographed. 901 represents theplane on which a camera 902 is positioned and photographs of the object900 are taken at a variety of positions on this plane. For example, theview position 906 yields the photograph 905 and the view position 903yields the photograph 904. Generally some mechanism is used to transporta camera from position to position in a sequential fashion using a 1 or2 dimensional translation stage to accomplish this. As before, thespacing and density of such 2-D views are generally controlled accordingto the information required for a certain type of hologram but in oneembodiment they form a regular 2-D matrix and in another a regularhorizontal 1-D array.

In both of the above cases restricted animation, which may betransferred to the final hologram, may be modeled by arranging that themodel 900 moves in a defined sense (representing such animation) asdifferent camera positions are selected on the plane 901, such camerapositions following sequential monotonic trajectories on the plane. Onobserving the final hologram, an observer following such sequentialmonotonic trajectory in the observation space will perceive theanimation.

Mathematical Definition of 3-D Data

The preferred embodiment defines a set of 2-D views of a real orcomputer represented object 900 on a certain viewing plane 901 (forseveral colours) and processes such views digitally to generate data(e.g. 904, 905) that is displayed on spatial light modulators which formpart of the holographic printer. Cartesian coordinates ξ and ζ may bedefined to represent respectively the x and y directions on theviewing/camera plane 901. The origin of this coordinate system may bedefined as the bottom left hand corner of 901. The plane 901 can bediscretized as follows: $\begin{matrix}\begin{matrix}{{\xi = {\left( {k - 1} \right)\frac{\Xi}{\left( {N_{K} - 1} \right)}}},} & {{k = 1},\ldots\quad,N_{K}}\end{matrix} & (1) \\\begin{matrix}{{\zeta = {\left( {g - 1} \right)\frac{\Theta}{\left( {N_{G} - 1} \right)}}},} & {{g = 1},\ldots\quad,N_{G}}\end{matrix} & (2)\end{matrix}$

-   -   where the integers k and g label perspective view locations on        901. A grid of (N_(K)×N_(G)) perspective views is therefore        envisaged covering the plane 901 which has dimensions Ξ×Θ (FIG.        10).

The Cartesian coordinates x and y may be defined to describe eachperspective view of size Q_(X)×Q_(Y) (e.g. 904, 905). Again an origin atthe bottom left-hand corner is used and discretization is as above:$\begin{matrix}{{x = {\left( {i - 1} \right)\frac{Q_{X}}{\left( {N_{1} - 1} \right)}}},\quad{i = 1},\ldots\quad,N_{I}} & (3) \\{{y = {\left( {j - 1} \right)\frac{Q_{Y}}{\left( {N_{J} - 1} \right)}}},\quad{j = 1},\ldots\quad,N_{J}} & (4)\end{matrix}$A grid of (N_(I)×N_(J)) pixels is therefore envisaged covering eachperspective view with each such view having dimensions of Q_(X)×Q_(Y)(FIG. 11).

If it is desired to model a full-parallax 3-D scene then the luminousintensity tensor is defined as ^(kg)I_(ij). This tensor represents thetotality of information describing the 3-D scene. It can either beprovided by multiple photographic data or as the output of a standardcommercial 3-D modeling program. In the case of horizontal parallaxholograms the index g is fixed and the luminous intensity tensor may bedefined simply as ^(k)I_(ij).

Transformation of Basic Data for H3 Writing

In order to discuss basic H3 transformation algorithms, it is necessaryto define three more coordinate systems. The H3 hologram may be regardedas being composed of many holographic pixels (N_(A)×N_(B)), the locationof each of which is described by the Cartesian system (X,Y). Adoptingthe notation, $\begin{matrix}{{X = {{\left( {\alpha - 1} \right)\frac{D_{3}}{\left( {N_{A} - 1} \right)}\quad\alpha} = 1}},\ldots\quad,N_{A}} & (5) \\{{Y = {{\left( {\beta - 1} \right)\frac{R_{3}}{\left( {N_{B} - 1} \right)}\quad\beta} = 1}},\ldots\quad,N_{B}} & (6)\end{matrix}$where D₃ represents the H3 hologram (horizontal) width and R₃ the H3hologram height (FIG. 11).

For the desired H2 hologram the same coordinate system as has beenpreviously introduced for the perspective views can be used, namely:$\begin{matrix}{{x = {\left( {i - 1} \right)\frac{D_{2}}{\left( {N_{I} - 1} \right)}}},\quad{i = 1},\ldots\quad,N_{I}} & (7) \\{{y = {\left( {j - 1} \right)\frac{R_{2}}{\left( {N_{J} - 1} \right)}}},\quad{j = 1},\ldots\quad,N_{J}} & (8)\end{matrix}$where it is arranged that Q_(X)=D₂=the (horizontal) width of the H2hologram and Q_(Y)=R₂=the height of the H2 (FIG. 10). This choiceamounts to a particular choice of how the cameras shown in FIGS. 9-11are set up or alternatively how the rendering output from commercial 3-Dprograms is configured. In the case of 3-D programs it is also thechoice of minimum rendering computation or what is referred to sometimesas a “centred camera”. Physically this choice amounts to generatingrendered 2-D perspective data only for the actual H2 hologram area. Thuseach camera shot of FIG. 11 is arranged to see the object 900 through awindow defined by the area of the H2 hologram. Alternatively, if thecamera views 904 and 905 are re-projected onto the H2 plane (1101) usingthe same paraxial camera optics as were used to generate thesephotographs then by the use of a suitable clipping window it can bearranged that both shots exactly fill the H2 hologram area at the H2plane—or equivalently points 1103, 1102, 1104 and 1105 on the H2 plane1101 may be constructed to correspond respectively to 1103, 1102, 1104and 1105 on the view-planes 904 and 905 (and all others).

As described above, digital data for each colour channel is written ontothe H3 hologram by displaying such data onto a miniature 2-D LCD displayand then illuminating such display with laser radiation and sharplyfocusing such radiation to form a holographic pixel near or at thesurface of the H3 plane. The optical objective that performs thisfocalization will be regarded as being perfectly paraxial for themoment. This makes it possible to derive a series of simple paraxialdata transformations. These transformations are then preferably modifiedfor the inclusion of finite optical objective distortion.

By assuming a paraxial optical objective between LCD and the H3, aprojected LCD image plane coincident with the viewing plane can bedefined which is geometrically similar to the LCD plane. The location ofa pixel on a given LCD image is therefore defined by its projected x andy Cartesian coordinates (u,v) on the viewing plane where,$\begin{matrix}{{u = {\left( {\mu - 1} \right)\frac{\Pi}{\left( {N_{M} - 1} \right)}}},\quad{\mu = 1},\ldots\quad,N_{M}} & (9) \\{{v = {\left( {\upsilon - 1} \right)\frac{\Sigma}{\left( {N_{V} - 1} \right)}}},\quad{\upsilon = 1},\ldots\quad,N_{V}} & (10)\end{matrix}$The parameters N_(M) and N_(V) are defined by the LCD used (typicallyN_(M) is 1024 and N_(V) is 768) although these parameters may bedegraded by doubling or tripling up on pixels if such high angularresolution is not required. These parameters together with the objectivefield of view essentially determine the angular resolution of the H3 andin all usual cases that of the H2. The parameters π and Σ respectivelyrepresent the projected horizontal and vertical dimensions of the LCD atthe viewing plane. A tensor quantity ^(μν)S_(αβ) may be defined whichwill be referred to hereinafter as the paraxial mask tensor. Thisquantity defines the luminous intensity (as a function of μ and ν) thatmust be written onto a given colour channel LCD for the H3 pixel definedby (α,β) assuming paraxial optics. In order to write an H3 hologram fromreadily available digital data a set of transformations must be derivedthat allow ^(μν)S_(αβ) to be calculated from ^(kg)I_(ij).H3 Paraxial Mask Tensor Transformations

The transformation laws that make the conversion from I to S depend onH2 viewing geometry considerations and the required H2 hologramparallax. For clarity several cases will be considered.

(I) Full Parallax Image with Fixed Rectangular Viewing Window

FIG. 15 shows an overhead section view of the H2 (1501), H3 (1502) andviewing window (1503). FIG. 16 shows a side view of the same situation.It is assumed that the H2, H3 and viewing window are parallel to oneanother and that they are centred. It is further assumed that theviewing window and camera plane are geometrically identical andcollocated. Both of these planes are of the same vertical and horizontalsize as the H2 hologram. It is apparent that Ξ=D₂ and Θ=R₂. The H2 andH3 planes are separated by a distance a and the viewing/camera and H2planes by a distance h.

The numerical data are rendered using a computational objective lenshaving the same horizontal effective field of view (FOV) as the paraxialFOV of the actual hologram writing objective (as apodised by the LCD)and h is chosen such that h=D₂ cot(θ/2) where Θ is the objective andrendering (horizontal) FOV. Since a centred camera model is used, forcamera position 1506 data is only rendered between the clipping planes1508 and 1509. Thus it is apparent from FIG. 15 that π=2D₂−2ε, whereε=αD₂/h, and with a centred camera (discussed above) Q_(x)=D₂.

The writing of the holographic pixel 1504, whose coordinates on the H3are (X,Y), and more specifically the individual ray, 1505, will now beconsidered. The brightness and colour information concerning this rayare contained in the camera shot taken at the horizontal cameracoordinate ξ (at 1506 since the viewing window is regarded as beinggeometrically identical to the camera tracking window) and correspondsto a horizontal picture coordinate of x at 1507 (since H2 is regarded asbeing geometrically identical to, and collocated with, each and everycamera picture window). Thusu=D ₂ −ε+w  (11)ξ=X−ε+w  (12)Using these two equations and the definitions of ξ, X and u thefollowing is obtained: $\begin{matrix}{{{\left( {\mu - 1} \right)\frac{\Pi}{\left( {N_{M} - 1} \right)}} = {D_{2} + {\left( {k - 1} \right)\frac{\Xi}{\left( {N_{K} - 1} \right)}} - {\left( {\alpha - 1} \right)\frac{D_{3}}{\left( {N_{A} - 1} \right)}}}},} & (13)\end{matrix}$which then leads to an index transformation rule for k: $\begin{matrix}\begin{matrix}{k = {{\frac{\left( {N_{K} - 1} \right)}{D_{2}}\frac{\left( {\alpha - 1} \right)\left( {D_{2} + {2ɛ}} \right)}{\left( {N_{A} - 1} \right)}} +}} \\{{{2\frac{\left( {N_{K} - 1} \right)}{D_{2}}\frac{\left( {\mu - 1} \right)\left( {D_{2} - ɛ} \right)}{\left( {N_{M} - 1} \right)}} - N_{K} + 2},}\end{matrix} & (14)\end{matrix}$which on the use of the relation ε=^(αD) ₂/h simplifies to$\begin{matrix}{k = {1 + {\left( {N_{K} - 1} \right)\left\lbrack {\frac{\left( {\alpha - 1} \right)\left( {1 + {2{a/h}}} \right)}{\left( {N_{A} - 1} \right)} + {2\frac{\left( {\mu - 1} \right)\left( {1 - {a/h}} \right)}{\left( {N_{M} - 1} \right)}} - 1} \right\rbrack}}} & (15)\end{matrix}$Now, by similar triangles it can be seen from FIG. 15 that$\begin{matrix}{\frac{h - a}{w} = {\frac{a}{X - ɛ - x}.}} & (16)\end{matrix}$Substituting the definitions of X and x the following is obtained:$\begin{matrix}{{\frac{\left( {\alpha - 1} \right)\left( {D_{2} + {2ɛ}} \right)}{\left( {N_{A} - 1} \right)} - ɛ - \frac{\left( {i - 1} \right)D_{2}}{\left( {N_{I} - 1} \right)}} = {\left\lbrack \frac{a}{h - a} \right\rbrack\left\lbrack {{2\frac{\left( {\mu - 1} \right)\left( {D_{2} - ɛ} \right)}{N_{M} - 1}} + ɛ - D_{2}} \right\rbrack}} & (17)\end{matrix}$from whence the index transformation rule for i is derived:$\begin{matrix}{i = {1 + \frac{\left( {N_{I} - 1} \right)\left( {\alpha - 1} \right)\left( {1 + \frac{2a}{h}} \right)}{\left( {N_{A} - 1} \right)} + \frac{\left( {N_{I} - 1} \right){a\left( {\frac{a}{h} - {2\left( {\mu - 1} \right)}} \right)}}{\left( {N_{M} - 1} \right)\left( {h - a} \right)}}} & (18)\end{matrix}$

In order to derive index transformation rules for g and j, it isnecessary to study FIG. 16 which shows a projection of rays in the y-zplane. As before 1501 represents the H2, 1502 the H3 and 1503 theviewing plane.

The assumption is made that the LCD used to write the digital data hasthe same height to length ratio as the viewing zone and the required H2hologram. This is a special case and will not always be true. However,it allows a simpler derivation of the equations to be presented beforegoing on to generalize. The numerical data are rendered using acomputational objective lens having the same effective field of view(FOV) in both the horizontal and vertical directions as that of theactual paraxial hologram writing objective (as apodised by the LCD).Therefore, it can be seen from FIG. 16 that Σ=2R₂−2δ, where δ=αR₂/h, andwith a centred camera (with camera clipping planes 1606 and 1607),Q_(Y)=R₂.

Now, with further reference to FIG. 16, it is necessary to considerwriting the holographic pixel 1504 whose coordinates on the H3 are (X,Y)and to consider the individual ray 1505. The brightness and colourinformation concerning this ray are contained in the camera shot takenat the vertical camera coordinate ç (at 1604 the viewing window isregarded as being geometrically identical to, and collocated with, thecamera tracking window) and corresponds to a vertical picture coordinateof y at 1608 (since H2 is regarded as being geometrically identical to,and collocated with, each and every camera picture window). Thusv=R ₂−δ+τ  (19)ç=Y−δ+τ  (20)Using these two equations and the definitions of ç, Y and v thefollowing is obtained: $\begin{matrix}{{{\left( {v - 1} \right)\frac{\Sigma}{\left( {N_{V} - 1} \right)}} = {R_{2} + {\left( {g - 1} \right)\frac{\Theta}{\left( {N_{G} - 1} \right)}} - {\left( {\beta - 1} \right)\frac{R_{3}}{\left( {N_{B} - 1} \right)}}}},} & (21)\end{matrix}$which then leads to an index transformation rule for g: $\begin{matrix}{{g = {{\frac{\left( {N_{G} - 1} \right)}{R_{2}}\frac{\left( {\beta - 1} \right)\left( {R_{2} + {2\delta}} \right)}{\left( {N_{B} - 1} \right)}} + {2\frac{\left( {N_{G} - 1} \right)}{R_{2}}\frac{\left( {v - 1} \right)\left( {R_{2} - \delta} \right)}{\left( {N_{V} - 1} \right)}} - N_{G} + 2}},} & (22)\end{matrix}$which on the use of the relation δ=αR₂/h simplifies to $\begin{matrix}{g = {1 + {\left( {N_{G} - 1} \right)\left\lbrack {\frac{\left( {\beta - 1} \right)\left( {1 + \frac{2a}{h}} \right)}{\left( {N_{B} - 1} \right)} + {2\frac{\left( {v - 1} \right)\left( {1 - \frac{a}{h}} \right)}{\left( {N_{V} - 1} \right)}} - 1} \right\rbrack}}} & (23)\end{matrix}$By similar triangles it can be seen from FIG. 16 that $\begin{matrix}{\frac{h - a}{\tau} = {\frac{a}{Y - \delta - y}.}} & (24)\end{matrix}$Substituting in the definitions of Y and y gives $\begin{matrix}{{\frac{\left( {\beta - 1} \right)\left( {R_{2} + {2\delta}} \right)}{\left( {N_{B} - 1} \right)} - \delta - \frac{\left( {j - 1} \right)R_{2}}{\left( {N_{J} - 1} \right)}} = {\left\lbrack \frac{a}{h - a} \right\rbrack\left\lbrack {{2\frac{\left( {v - 1} \right)\left( {R_{2} - \delta} \right)}{N_{V} - 1}} + \delta - R_{2}} \right\rbrack}} & (25)\end{matrix}$from whence the index transformation rule for j is derived:$\begin{matrix}{j = {1 + \frac{\left( {N_{J} - 1} \right)\left( {\beta - 1} \right)\left( {1 + \frac{2a}{h}} \right)}{\left( {N_{B} - 1} \right)} + {\frac{\left( {N_{J} - 1} \right){a\left( {\frac{a}{h} - {2\left( {v - 1} \right)}} \right)}}{\left( {N_{V} - 1} \right)\left( {h - a} \right)}.}}} & (26)\end{matrix}$

The H3 mask transformation for a double parallax hologram of viewingwindow size equal to H2 hologram size under the assumption that the LCDaspect ratio equals the H2 hologram aspect ratio can therefore be givenas:^(μν)S_(αβ)=^(kg)I_(ij) when 0<k≦N_(K) and 0<g≦N_(G)  (27)

-   -   and 0<i≦N_(I) and 0<j≦N_(J)=0 otherwise        where $\begin{matrix}        {k = {1 + {\left( {N_{K} - 1} \right)\left\lbrack {\frac{\left( {\alpha - 1} \right)\left( {1 + \frac{2a}{h}} \right)}{\left( {N_{A} - 1} \right)} + {2\frac{\left( {\mu - 1} \right)\left( {1 - \frac{a}{h}} \right)}{\left( {N_{M} - 1} \right)}} - 1} \right\rbrack}}} & (28) \\        {i = {1 + \frac{\left( {N_{I} - 1} \right)\left( {\alpha - 1} \right)\left( {1 + \frac{2a}{h}} \right)}{\left( {N_{A} - 1} \right)} + \frac{\left( {N_{I} - 1} \right){a\left( {\frac{a}{h} - {2\left( {\mu - 1} \right)}} \right)}}{\left( {N_{M} - 1} \right)\left( {h - a} \right)}}} & (29) \\        {j = {1 + \frac{\left( {N_{J} - 1} \right)\left( {\beta - 1} \right)\left( {1 + \frac{2a}{h}} \right)}{\left( {N_{B} - 1} \right)} + \frac{\left( {N_{J} - 1} \right){a\left( {\frac{a}{h} - {2\left( {v - 1} \right)}} \right)}}{\left( {N_{V} - 1} \right)\left( {h - a} \right)}}} & (30) \\        {g = {1 + {{\left( {N_{G} - 1} \right)\left\lbrack {\frac{\left( {\beta - 1} \right)\left( {1 + \frac{2a}{h}} \right)}{\left( {N_{B} - 1} \right)} + {2\frac{\left( {v - 1} \right)\left( {1 - \frac{a}{h}} \right)}{\left( {N_{V} - 1} \right)}} - 1} \right\rbrack}.}}} & (31)        \end{matrix}$        (II) General Aspect Ratio

A particular H3 mask transformation for the case of a fixed choice ofhologram aspect ratio has been derived above. The constraint on aspectratio will now be relaxed. The derivation for the index rules for k andi remain unchanged as the choice of choosing h such that h=D₂ cot(θ/2)where θ is the objective horizontal FOV and π=2D₂−2ε can be adopted.However, the index rules for g and j appear no longer to be the same asit is not possible to also choose h by requiring that h=R₂ cot(ω/2)where ω is the vertical objective FOV and Σ=2R₂−2δ (unless of course theaspect ratio of the H2 and LCD were the same).

On examination of FIG. 17 it can be seen that only equation 19 ischanged out of 19, 20 and 24. This equation now becomesν=Σ/2+τ.  (32)Using equation 20 and the definitions of v and Y the followingexpression is obtained: $\begin{matrix}{\frac{\left( {v - 1} \right)\Sigma}{N_{V} - 1} = {\frac{\Sigma}{2} + \frac{\left( {g - 1} \right)\Theta}{N_{G} - 1} - \frac{\left( {\beta - 1} \right)R_{3}}{N_{B} - 1} + \delta}} & (33)\end{matrix}$which on the substitution of the auxiliary relationsΘ=R₂δ=αR ₂ /hR₃ =R ₂−2δ  (34)leads to the required index equation for g $\begin{matrix}{g = {1 + {{\left( {N_{G} - 1} \right)\left\lbrack {{\frac{\Sigma}{R_{2}}\left\{ {\frac{\left( {v - 1} \right)}{N_{V} - 1} - \frac{1}{2}} \right\}} + {\frac{\left( {\beta - 1} \right)}{N_{B} - 1}\left\{ {1 - \frac{2a}{h}} \right\}} - \frac{a}{h}} \right\rbrack}.}}} & (35)\end{matrix}$

Since equation 24 remains unchanged for the general aspect ratio case,the index rule for j also remains the same. The H3 mask transformationfor a double parallax hologram of viewing window size equal to H2hologram size for a general LCD and hologram aspect ratio may thereforebe given as:^(μν)S_(αβ)=^(kg)I_(ij) when 0<k≦N_(K) and 0<g≦N_(G)  (36)

-   -   and 0<i≦N_(I) and 0<j≦N_(J)=0 otherwise        where $\begin{matrix}        {k = {1 + {\left( {N_{K} - 1} \right)\left\lbrack {\frac{\left( {\alpha - 1} \right)\left( {1 + \frac{2a}{h}} \right)}{\left( {N_{A} - 1} \right)} + {2\frac{\left( {\mu - 1} \right)\left( {1 - \frac{a}{h}} \right)}{\left( {N_{M} - 1} \right)}} - 1} \right\rbrack}}} & (37) \\        {i = {1 + \frac{\left( {N_{I} - 1} \right)\left( {\alpha - 1} \right)\left( {1 + \frac{2a}{h}} \right)}{\left( {N_{A} - 1} \right)} + \frac{\left( {N_{I} - 1} \right){a\left( {\frac{a}{h} - {2\left( {\mu - 1} \right)}} \right)}}{\left( {N_{M} - 1} \right)\left( {h - a} \right)}}} & (38) \\        {j = {1 + \frac{\left( {N_{J} - 1} \right)\left( {\beta - 1} \right)\left( {1 + \frac{2a}{h}} \right)}{\left( {N_{B} - 1} \right)} + \frac{\left( {N_{J} - 1} \right){a\left( {\frac{a}{h} - {2\left( {v - 1} \right)}} \right)}}{\left( {N_{V} - 1} \right)\left( {h - a} \right)}}} & (39) \\        {g = {1 + {{\left( {N_{G} - 1} \right)\left\lbrack {{\frac{\Sigma}{R_{2}}\left\{ {\frac{\left( {v - 1} \right)}{N_{V} - 1} - \frac{1}{2}} \right\}} + {\frac{\left( {\beta - 1} \right)}{N_{B} - 1}\left\{ {1 - \frac{2a}{h}} \right\}} - \frac{a}{h}} \right\rbrack}.}}} & (40)        \end{matrix}$        (III) General Rectangular Viewing Window (Ξ×Θ)

The more complicated case of a general rectangular viewing zone that isnot of the same dimensions as the H2 hologram will now be considered.

FIG. 18(a) shows an overhead section view of the H2 (1501), H3 (1502)and viewing window (1503). FIG. 19(a) shows a side view of the samesituation. As before it is assumed that the H2, H3 and viewing windoware parallel to one another and that they are centred. It is furtherassumed, as before, that the viewing window and camera plane aregeometrically identical and collocated. However, these planes are nolonger of the same vertical and horizontal size as the H2 hologram butare rather of horizontal dimension Ξ and vertical dimension Θ. As beforethe H2 and H3 planes are separated by a distance a and theviewing/camera and H2 planes by a distance h.

The numerical data is rendered using a computational objective lenshaving the same effective field of view (FOV) as that of the actualparaxial hologram writing objective (as apodised by the LCD) but now his chosen such that generally Ξ<2 h tan(θ/2)−D₂ and Θ<2 h tan(ω/2)−R₂where θ is the horizontal objective FOV and ω is the vertical objectiveFOV (both as apodised by the LCD). This is different to the situationwhen a specific h was chosen to ensure 100% utilization of the LCD inthe horizontal direction (i.e. h=D₂ cot(θ/2)). As before it is arrangedthat Q_(x)=D₂ (centred camera).

With reference to FIG. 18 a, the writing of the holographic pixel 1504whose coordinates on the H3 are (X,Y) and the individual ray 1505 willbe considered. The brightness and colour information concerning this rayare contained in the camera shot taken at the horizontal cameracoordinate ξ (at 1506 since the viewing window is regarded as beinggeometrically identical to the camera tracking window) and correspondsto a horizontal picture coordinate of x at 1507 (as the H2 is regardedas being geometrically identical to, and collocated with, each and everycamera picture window). Thus $\begin{matrix}{u = {\frac{\Pi}{2} + w}} & (41) \\{\xi = {X + w - ɛ + {\frac{\Xi - D_{2}}{2}.}}} & (42)\end{matrix}$Using these two equations and the definitions of ξ, X and u thefollowing is obtained: $\begin{matrix}{{\left( {k - 1} \right)\frac{\Xi}{\left( {N_{K} - 1} \right)}} = {{\left( {\mu - 1} \right)\frac{\Pi}{\left( {N_{M} - 1} \right)}} + {\left( {\alpha - 1} \right)\frac{D_{3}}{\left( {N_{A} - 1} \right)}} - \frac{\Pi}{2} + \frac{\Xi - D_{2}}{2} - {ɛ.}}} & (43)\end{matrix}$Using the auxiliary relations (readily evident from FIG. 18 a)$\begin{matrix}{{\frac{\Pi}{2\left( {h - a} \right)} = \frac{ɛ}{a}}{D_{3} = {D_{2} + {2ɛ}}}} & (44)\end{matrix}$allows the following k index rule to be derived: $\begin{matrix}{k = {1 + {\left( {N_{K} - 1} \right){\left\{ {{\frac{1}{2}\left\lbrack {1 - \frac{D_{2}}{\Xi} - \frac{\Pi\quad h}{\left( {h - a} \right)\Xi}} \right\rbrack} + \frac{\left( {\alpha - 1} \right)\left( {D_{2} + \frac{a\quad\Pi}{h - a}} \right)}{\Xi\left( {N_{A} - 1} \right)} + \frac{\left( {\mu - 1} \right)\Pi}{\left( {N_{M} - 1} \right)\Xi}} \right\}.}}}} & (45)\end{matrix}$By similar triangles, with reference to FIG. 18(a), it can now beobserved that: $\begin{matrix}{\frac{w}{h - a} = \frac{X - x - ɛ}{a}} & (46)\end{matrix}$from whence, using equations 41 and 44, the i index rule is obtained:$\begin{matrix}{i = {1 + {\left( {N_{I} - 1} \right){\left\{ {\frac{\left( {\alpha - 1} \right)\left( {1 + \frac{a\quad\Pi}{D_{2}\left( {h - a} \right)}} \right)}{\left( {N_{A} - 1} \right)} - \frac{a\quad{\Pi\left( {\mu - 1} \right)}}{{D_{2}\left( {h - a} \right)}\left( {N_{M} - 1} \right)}} \right\}.}}}} & (47)\end{matrix}$Similarly, exactly the same derivation from FIG. 19(a) may be performedin the vertical plane to derive index rules for j and g. Thus the(paraxial) mask transformation for a general sized rectangular viewingwindow (Ξ×Θ) may be given as:^(μν)S_(αβ)=^(kg)I_(ij) when 0<k≦N_(K) and 0<g≦N_(G)  (48)

-   -   and 0<i≦N_(I) and 0<j<N_(J)=0 otherwise        where $\begin{matrix}        {k = {1 + {\left( {N_{K} - 1} \right)\left\{ {{\frac{1}{2}\left\lbrack {1 - \frac{D_{2}}{\Xi} - \frac{\Pi\quad h}{\left( {h - a} \right)\Xi}} \right\rbrack} + \frac{\left( {\alpha - 1} \right)\left( {D_{2} + \frac{a\quad\Pi}{h - a}} \right)}{\Xi\left( {N_{A} - 1} \right)} + \frac{\left( {\mu - 1} \right)\Pi}{\left( {N_{M} - 1} \right)\Xi}} \right\}}}} & (49) \\        {i = {1 + {\left( {N_{I} - 1} \right)\left\{ {\frac{\left( {\alpha - 1} \right)\left( {1 + \frac{a\quad\Pi}{D_{2}\left( {h - a} \right)}} \right)}{\left( {N_{A} - 1} \right)} - \frac{a\quad{\Pi\left( {\mu - 1} \right)}}{{D_{2}\left( {h - a} \right)}\left( {N_{M} - 1} \right)}} \right\}}}} & (50) \\        {g = {1 + {\left( {N_{G} - 1} \right)\left\{ {{\frac{1}{2}\left\lbrack {1 - \frac{R_{2}}{\Theta} - \frac{\Sigma\quad h}{\left( {h - a} \right)\Theta}} \right\rbrack} + \frac{\left( {\beta - 1} \right)\left( {R_{2} + \frac{a\quad\Sigma}{h - a}} \right)}{\Theta\left( {N_{B} - 1} \right)} + \frac{\left( {v - 1} \right)\Sigma}{\left( {N_{V} - 1} \right)\Theta}} \right\}}}} & (51) \\        {j = {1 + {\left( {N_{J} - 1} \right){\left\{ {\frac{\left( {\beta - 1} \right)\left( {1 + \frac{a\quad\Sigma}{R_{2}\left( {h - a} \right)}} \right)}{\left( {N_{B} - 1} \right)} - \frac{a\quad{\Sigma\left( {v - 1} \right)}}{{R_{2}\left( {h - a} \right)}\left( {N_{V} - 1} \right)}} \right\}.}}}} & (52)        \end{matrix}$

It is worth noting that the size of the H3 hologram can be reduced bythe choice of a slightly different coordinate system. This choice isapplicable to both the vertical and horizontal planes and is shown inFIGS. 18 b and 19 b. In the case of the horizontal plane, equation 44 ismodified so: $\begin{matrix}{D_{3} = {D_{2} + {\frac{\Xi - D_{2}}{h}.}}} & (53)\end{matrix}$Likewise equation 42 becomes $\begin{matrix}{\xi = {\frac{\Xi - D_{2}}{2} - \frac{a\left( {\Xi - D_{2}} \right)}{2h} + X + w}} & (54)\end{matrix}$and equation 46 becomes $\begin{matrix}{\frac{w}{h - a} = {\frac{X - x}{a} - {\frac{\left( {\Xi - D_{2}} \right)}{2h}.}}} & (55)\end{matrix}$Using these modified equations and the method described above a set ofsimilar equations to 48-52 may be derived for such a modified H3.

It is to be noted that h was chosen such that generally Ξ<2 htan(θ/2)−D₂ and Θ<2 h tan(ω/2)−R₂ where θ is the horizontal objectiveFOV and ω is the vertical objective FOV (both as apodised by the LCD).This had enabled the LCD to write any format of hologram having anyformat of viewing window, but at the expense of not using all of theLCD. Thus generally one wants to chose either Ξ≈2 h tan(θ/2)−D₂ or Θ≈2 htan(ω/2)−R₂.

(IV) Single Parallax Limit

So far the general case of a full parallax (H2) hologram has beendiscussed. It is possible to simplify the general parallax masktransformations hereto presented for the single parallax case.Specifically, it is noted that ^(kg)I_(ij)=^(k)I_(ij) ∀g where^(k)I_(ij) represents the camera information corresponding to avertically central camera position. Using this relation it is possibleto simplify any general parallax mask transformation in order to arriveat the simpler single parallax mask transformations. In general thetransformation rules for the g index are simply eliminated and replacedby vertical field-of-view restrictions on S.

(V) Unconstrained Viewing Window

The definition of a rectangular viewing window is not mandatory. Rather,by using all of the LCD, a class of mask transformation can be derivedthat lets every pixel in the H2 radiate over the same solid angle.Generally this embodiment is less preferred as the viewer may see anincomplete (H2) hologram image from many positions. With a rectangularwindow this is not the case—either the image is entirely viewable by theobserver or it is not. It will be clear to those skilled in the art howto reproduce the above arguments for such a case.

Generalization to Non-Paraxial Optics

In useful objectives of large FOV that may be used to write H3holograms, there is inevitably present significant optical distortion.It has been disclosed in WO01/04716 that for a particularly useful classof objectives, as the FOV was increased, so the optical distortionassociated with a finite 5^(th) Seidel coefficient also increased. Ifthe object and image planes of a given objective as in FIG. 20 arecompared it is possible to characterize this distortion by the followingtransformation: $\begin{matrix}\begin{matrix}{u = {\frac{\Pi}{2} + {\left( {U - \frac{\Pi}{2}} \right){\psi\left( {U,V} \right)}}}} \\{v = {\frac{\Sigma}{2} + {\left( {V - \frac{\Sigma}{2}} \right){\psi\left( {U,V} \right)}}}}\end{matrix} & (56) \\{where} & \quad \\{{\psi\left( {U,V} \right)} = {f\left( \sqrt{\left\{ {U - \frac{\prod}{2}} \right\}^{2} + \left\{ {V - \frac{\sum}{2}} \right\}^{2}} \right)}} & (57)\end{matrix}$and f is a general function that describes the distortion. Theseequations may also be interpreted as a transformation from real toparaxial object planes. Thus, by simply replacing the expressions$\begin{matrix}{{u = {\left( {\mu - 1} \right)\frac{\Pi}{\left( {N_{M} - 1} \right)}}},\quad{\mu = 1},\ldots\quad,N_{M}} & (58) \\{{v = {\left( {\upsilon - 1} \right)\frac{\Sigma}{\left( {N_{V} - 1} \right)}}},\quad{\upsilon = 1},\ldots\quad,N_{V}} & (59) \\{by} & \quad \\\begin{matrix}{{u = {{\frac{\Pi}{2} + {\left\lbrack {{\left( {\mu - 1} \right)\frac{\Pi}{\left( {N_{M} - 1} \right)}} - \frac{\Pi}{2}} \right\rbrack\psi_{\mu\quad v}\quad\mu}} = 1}},\ldots\quad,N_{M}} \\{{v = {{\frac{\Sigma}{2} + {\left\lbrack {{\left( {v - 1} \right)\frac{\Sigma}{\left( {N_{V} - 1} \right)}} - \frac{\Sigma}{2}} \right\rbrack\psi_{\mu\quad v}\quad\upsilon}} = 1}},\ldots\quad,N_{V}}\end{matrix} & (60)\end{matrix}$in all preceding equations the paraxial mask transformations may beconverted into finite distortion mask transformations. Hence, by way ofexample, the above relation can be substituted for u in equation 11 inorder to derive a modified equation 13 and from there a modified k indexrule (which would be the finite distortion k index rule). It is alsopossible to derive any finite distortion mask transformation using theserules and the information that has been hereto presented concerningparaxial mask transformations.

It is also possible to apply a simple distortion correction, based onthe above equations after a paraxial mask transformation has beenapplied. Thus the paraxial mask tensor ^(μν)S_(αβ) may be calculated andthen a distortion compensation transformation applied^(ση)T_(αβ)=^(μo)S_(αβ)  (61)where $\begin{matrix}\begin{matrix}{\sigma = {\frac{N_{M} + 1}{2} + {\left\{ {\mu - 1 - \frac{\left( {N_{M} - 1} \right)}{2}} \right\}\psi_{\mu\quad v}}}} \\{\eta = {\frac{N_{V} + 1}{2} + {\left\{ {v - 1 - \frac{\left( {N_{V} - 1} \right)}{2}} \right\}\psi_{\mu\quad v}}}}\end{matrix} & (62)\end{matrix}$to arrive at the final finite objective mask tensor T.Other Distortions

Many other image distortions may arrive in a holographic printer. Suchdistortions may be due to emulsion swelling due to chemical processing,different wavelengths of reconstruction and recording, refractive indexeffects within the holographic material and changes in replay andrecording reference beam angles, to name just a few. Without exceptionall of these distortions may be written in terms of a pixel swaptransformation as with the finite objective distortion case. However,most distortions lack the symmetry properties of this particular case.

By combining all pixel swaps into a single finite distortion masktransformation it is possible to minimize computation and mostimportantly to minimize interpellation error. This is because thevarious indices such as μ, ν, α, β, k and g are integers and yet therules such as equation 37 contain real coefficients. As such atruncation error is encountered each time an index rule is applied inthe calculation of the mask transformation. If many index swapping rulesare applied, one after the other, one for each distortion and one forthe paraxial mask transformation, then errors are accumulated. Byincorporating in a single transformation describing all of thedistortions present in the system it is possible to eliminate this indextruncation accumulation.

Generalization to Full Colour

The algorithms presented above are equally applicable to each and everycolour component hologram and its data. Where different opticaldistortions in the printer exist for the different writing wavelengthsit is clear that care must be taken in order to use the correctdistortion functions for each colour channel. Colour mixing andbalancing may be done both at the H3 and H2 stage and the relativeenergies in each chromatic channel should be adjusted according to thedesired visual result of the final hologram.

Limits

As the parameter a of FIG. 15 approaches zero the limit of“direct-write”—or the 1-step digital hologram limit—is arrived at. TheH3 then written is a transmission hologram rather than a reflectionhologram although the object data then recorded on this hologram is thesame object data that would be recorded using the direct-write (1-step)technique.

As the parameter a approaches “h” the limit of “H1 master-write” isarrived at. Here the object data now written on the H3 is the same asthe object data written with the Master-Write technique.

It will be appreciated that according to the preferred embodiment theseextreme limits are not used. Rather, by using a general case in which0<a<h many of the problems inherent with the known devices can besolved.

Although the preferred embodiment has been discussed above, it isapparent that various modifications may be made. For example, manydifferent types of laser may be used. Pulsed lasers are particularlypreferable as these lasers render the resulting printer immune fromvibration. However, CW lasers may also be used for certain applicationsif the exposure time of a given holographic pixel or super-pixel is keptshort enough. Thus, for example HeNe, Krypton, Argon, Neodymium, dye orHeCd lasers may be employed.

A wide variety of pulsed laser sources may be used. Lasers that producechromatic emissions that when added together (as in the standardchromaticity chart) produce a wide range of visually perceived coloursare preferred. In addition conventional light sources are expected to beused for illuminating holograms made with such chromatic emissions andtherefore the photographic recording materials used should be sensitiveto these emissions.

With these considerations in mind the mechanism that has been describedabove by which the blue laser emission is generated may be replaced by aNd:YAG oscillator and amplifier(s) functioning at 946 nm and a means forfrequency doubling to 473 nm. This emission has advantages of lowerRaleigh scattering and better visual perception. Clearly similaremissions based the atomic transitions of Neodymium in matrices otherthan YAG may be employed.

The mechanism that has been described above by which both the blue andred laser emissions are generated may be replaced by a Tm doped laseroscillator and amplifier(s). For example, Tm:YAL may be used such asKYb_(0.45)Y_(0.43)Tm_(0.07)(WO₄)₂ functioning at 1850-1970 nm and ameans for frequency tripling to 617-657 nm and quadrupling to 463-493nm. These emissions have the advantage of better visual perception.

Other pulsed or CW laser sources may be used in combination with H2emulsion swelling, H2 reference beam angle adjustment and digital datadistortion correction in order to produce undistorted white-lightviewable holograms that replay at different wavelengths than theirrecording wavelengths.

In most cases holograms must be displayed using a point source. Thismeans that the replay reference beam is generally diverging and thuslight rays hitting the final hologram on replay are not all at the sameangle. In the above discussion a preferred embodiment has been disclosedwherein the H2 reference beam angle and the H2 reference beam divergencefor each chromatic component remain constant during the H3:H2 transfer.However, the arrangement can be modified so that both the H2 referencebeam divergence and the H2 reference beam (altitudinal and azimuthal)angles change from super-pixel to super-pixel. In this way the referenceray geometry at recording may be precisely matched to the reference raygeometry on final replay.

If the replay point source is far enough away and the H2 super-pixel issmall then only the reference beam angles (altitudinal and azimuthal)need be changed. As the replay point source becomes closer to the finalhologram, however, if the H2 reference beam divergence on recording isnot adjusted at each super-pixel location, image blurring and/ordistortion may occur.

The embodiment described with reference to FIG. 12 may be modified bythe insertion of a method for changing the reference beam angle anddivergence between elements 1252 and 1251 (and similar methods for theother 2 colour channels). Care must be taken to ensure that theresulting modified reference beam hits its desired target (in this casethe zone 1252) with sufficient positional stability. In this way thereference beam 1275 is always directed towards zone 1252 and yet thealtitudinal and azimuthal angles of incidence of 1275 at 1252, as wellas (optionally) the divergence of 1275, are controlled and changed atevery laser shot (and similarly for the other two colour channels).

This technique is also important for when a large hologram is to beconstructed from many small holographic tiles. In this case H2 referencebeam control is highly desirable.

In some cases the need for adjusting the beam divergence at each H2super-pixel can be eliminated by pre-distortion of the data and someadjustment of local colour balance.

For each H2 emulsion type there generally exists an optimum H3/H2 energyratio for each colour and an optimum total energy for each colour. Itmay be desired to use the same H3 to write H2 holograms on differentemulsions that are designed for different viewing conditions (i.e. lightlocations). In many conventional devices (e.g. contact copying) thisflexibility is not provided for.

By use of modern thermoplastics H3 transmission holograms can berecorded without the need for chemical processing and without the needfor removal of the H3 from the printing machine. A thermoplastic H3 maybe overwritten and may thus form a semi-permanent part of the printer.In other cases a thermoplastic H3 may be loaded into the printer as aroll which is replaced from time to time. In other cases such a roll maybe used to store several H3 holograms and the printer control system mayselect which one to load for H3:H2 printing.

Photopolymers may also be used for the H3, in which case opticalprocessing accessories may be included within the printer and thephotopolymer may be installed in a cartridge or roll system that is tobe replaced from time to time.

The preferred embodiment may be modified to produce reflection type H3holograms by inclusion of suitable mirrors within the space between theH3 and H2 during copy. The mirrors direct various chromatic referencebeams to the zones 1252 and 1224 etc on the H2 from the side of the H3(and hence the hologram is a reflection hologram). Generally this is aless preferred embodiment as such mirrors severely restrict the minimumH3:H2 distance attainable.

In the preferred embodiment symmetric super-pixels are used. However,with the availability of larger laser energies on H3:H2 transfer asuper-pixel that is essentially rectangular wherein one dimension issmall compared to the hologram linear dimension and the other dimensionwhich is now equal to the linear dimension of the H2 hologram. In thisway a 1-dimensional set of displacements is performed during H3:H2transfer instead of a 2-dimensional set i.e. the H3 is transferred tothe H2 slit by slit, instead of rectangle by rectangle.

The use of highly asymmetric super-pixels may only be performed in onedirection as it is required, for example, that the zeroth ordertransmitted radiation produced by 1217 is occluded by the slit 1221.

Where H3:H2 transfers must be accomplished very fast then highlyasymmetric super-pixels are to be preferred.

1. A 2-step holographic printer wherein in a first mode of operationsaid holographic printer produces one or more intermediate holograms(H3) and wherein in a second mode of operation said holographic printerproduces a white light viewable hologram (H2) from said one or moreintermediate holograms (H3).
 2. A 2-step holographic printer as claimedin claim 1, further comprising one, two or more than two pulsed lasersources.
 3. A 2-step holographic printer as claimed in claim 2, whereina pulsed laser source produces a laser emission having a wavelengthselected from the group consisting of: (i) 946 nm; (ii) 1047 nm; (iii)1053 nm; (iv) 1064 nm; (v) 1070 nm; (vi) 1080 nm; (vii) 1313 nm; (viii)1319 nm; (ix) 1338 nm; (x) 1341 nm; (xi) 1351 nm; and (xii) 1850-1970nm.
 4. A 2-step holographic printer as claimed in claim 3, wherein alaser emission is frequency doubled to a wavelength selected from thegroup consisting of: (i) 473 nm; (ii) 523.6 nm; (iii) 526 nm; (iv) 532nm; (v) 535 nm; (vi) 539.8 nm; (vii) 656.5 nm; (viii) 659 nm; (ix) 669nm; (x) 670.7 nm; and (xi) 675.5 nm.
 5. A 2-step holographic printer asclaimed in claim 3, wherein a laser emission is frequency tripled to awavelength selected from the group consisting of: (i) 437.7 nm; (ii) 440nm; (iii) 446.0 nm; (iv) 447.1 nm; (v) 450.3 nm; and (ii) 617-657 nm. 6.A 2-step holographic printer as claimed in claim 3, wherein a laseremission is frequency quadrupled to a wavelength in the range 463-493nm.
 7. A 2-step holographic printer as claimed in claim 2, wherein apulsed laser source is selected from the group consisting of: (i)Nd:BEL; (ii) Nd:YAG; (iii) Nd:YAP; and (iv) Nd:YLF.
 8. A 2-stepholographic printer as claimed in claim 2, wherein a pulsed laser sourceis selected from the group consisting of: (i) Tm:YAG; (ii) Tm:YAL; and(iii) Thulium in a host matrix of Potassium Yttrium Ytterbium Tungstate.9. A 2-step holographic printer as claimed in claim 2, wherein at leastone pulsed laser source is configured to produce laser emissions ofsingle longitudinal mode.
 10. A 2-step holographic printer as claimed inclaim 2, wherein at least one pulsed laser source is configured toproduce laser emissions having a temporal coherence length greater than1 mm.
 11. A 2-step holographic printer as claimed in claim 2, wherein atleast one pulsed laser source comprises a means for modifying the laseremission wavelength by Raman scattering or Raman amplification.
 12. A2-step holographic printer as claimed in claim 1, further comprising oneor more CW laser sources.
 13. A 2-step holographic printer as claimed inclaim 12, wherein said laser source is selected from the groupconsisting of: (i) HeNe laser; (ii) Krypton laser; (iii) Argon laser;(iv) Neodymium laser; (v) dye laser; and (vi) HeCd laser.
 14. A 2-stepholographic printer as claimed in claim 1, wherein red and/or greenand/or blue laser beams are generated for writing holograms.
 15. A2-step holographic printer as claimed in claim 14, wherein said redlaser beam has a wavelength in the range 615-680 nm, said green laserbeam has a wavelength in the range 510-550 nm, and said blue laser beamhas a wavelength in the range 430-480 nm.
 16. A 2-step holographicprinter as claimed in claim 1, wherein said final white light viewablehologram comprises an RGB white light viewable reflection hologram. 17.A 2-step holographic printer as claimed in claim 1, further comprisingone or more spatial light modulators onto which digital data isdisplayed.
 18. A 2-step holographic printer as claimed in claim 17,wherein said digital data is derived from a real model.
 19. A 2-stepholographic printer as claimed in claim 17, wherein said digital data isderived from a 3-D computer model.
 20. A 2-step holographic printer asclaimed in claim 17, wherein said digital data is mathematicallytransformed to correct for optical distortion.
 21. A 2-step holographicprinter as claimed in claim 20, wherein said optical distortion isselected from the group consisting of: (i) H2 emulsion swelling onhologram processing; (ii) reference beam angle errors; (iii) finiteemulsion refractive index and emulsion refractive index not equallingrecording material substrate refractive index; (iv) required H2 replaywavelength not equalling recording wavelength; (v) required H2 replayreference angle not equalling recording reference angle; and (vi)intrinsic optical distortion of the printer including distortion due tothe principle objective(s).
 22. A 2-step holographic printer as claimedin claim 20, wherein said digital data is mathematically transformed bya single simple pixel swap that operates between an initial image dataset and a data set displayed on said one or more spatial lightmodulators.
 23. A 2-step holographic printer as claimed in claim 20,wherein said digital data is mathematically transformed by a series ofsimple pixel swaps.
 24. A 2-step holographic printer as claimed in claim1, wherein said one or more intermediate holograms (H3) are selectedfrom a group consisting of: (i) a transmission hologram, and (ii) areflection hologram.
 25. A 2-step holographic printer as claimed inclaim 24, wherein said one or more intermediate holograms (H3) areformed on a first substrate.
 26. A 2-step holographic printer as claimedin claim 1, wherein said one or more intermediate holograms (H3)comprise a transmission hologram; wherein said one or more intermediateholograms (H3) are formed on a first substrate; and wherein said firstsubstrate is selected from the group consisting of: (i) a photosensitivemedium (1219); (ii) a thermoplastic substrate; (iii) a photopolymersubstrate; and (v) a silver halide emulsion coated substrate. 27-28.(cancelled).
 29. A 2-step holographic printer as claimed in claim 1,wherein said one or more intermediate holograms (H3) comprise areflection hologram; wherein said one or more intermediate holograms(H3) are formed on a first substrate; and wherein said first substratecomprises a photosensitive medium.
 30. A 2-step holographic printer asclaimed in claim 25, further comprising positioning means forpositioning said first substrate so that a holographic pixel is writtenon said first substrate.
 31. A 2-step holographic printer as claimed inclaim 30, wherein said positioning means moves said first substrate sothat an array of holographic pixels is formed thereon.
 32. A 2-stepholographic printer as claimed in claim 31, wherein different colourholographic pixels are recorded at the same position on said firstsubstrate so that said different colour holographic pixels overlap oneanother.
 33. A 2-step holographic printer as claimed in claim 31,wherein different colour holographic pixels are recorded at differentpositions on said first substrate so that said different colourholographic pixels do not substantially overlap one another.
 34. A2-step holographic printer as claimed in claim 2, wherein in said secondmode the output from said pulsed laser sources is amplified.
 35. A2-step holographic printer as claimed in claim 1, wherein in said secondmode a first order diffracted beam is produced due to said intermediatehologram (H3).
 36. A 2-step holographic printer as claimed in claim 25,wherein in said second mode a second substrate on which said white lightviewable hologram (H2) is to be written is positioned parallel to saidfirst substrate.
 37. A 2-step holographic printer as claimed in claim36, wherein said second substrate is positioned at a distance d fromsaid first substrate wherein d is greater than zero and less than thedistance between the camera (H1) plane and the H2 plane.
 38. A 2-stepholographic printer as claimed in claim 36, wherein said secondsubstrate is positioned at a distance d from said first substratewherein d is greater than zero and less than ¼ of the height of said oneor more intermediate holograms.
 39. A 2-step holographic printer asclaimed in claim 36, wherein said second substrate is positioned at adistance d from said first substrate wherein d is greater than zero andless than ¼ of the width of said one or more intermediate holograms. 40.A 2-step holographic printer as claimed in claim 36, further comprisinga mask arranged adjacent said second substrate so that a portion of adiffracted beam illuminates said second substrate.
 41. A 2-stepholographic printer as claimed in claim 36, wherein a zeroth orderdiffracted beam is substantially prevented from illuminating said secondsubstrate.
 42. A 2-step holographic printer as claimed in claim 36,further comprising one or more line-pass optical filters (1224) placedbetween the first substrate and the second substrate.
 43. A 2-stepholographic printer as claimed in claim 42, wherein said one or moreline-pass optical filters (1224) comprise an interference filter.
 44. A2-step holographic printer as claimed in claim 36, wherein super-pixelscomprising superimposed red, green and blue holographic pixels arewritten on to said second substrate.
 45. A 2-step holographic printer asclaimed in claim 44, wherein said super-pixels do not substantiallyoverlap.
 46. A 2-step holographic printer as claimed in claim 44,wherein said super-pixels partially overlap.
 47. A 2-step holographicprinter as claimed in claim 1, wherein said white light viewablehologram (H2) is a reflection hologram.
 48. A hologram produced by a2-step holographic printer as claimed in claim
 1. 49. A hologram asclaimed in claim 48, wherein said hologram is selected from the groupconsisting of: (i) a single parallax hologram; and (ii) a full parallaxhologram.
 50. A method of printing a hologram, comprising: producing oneor more intermediate holograms (H3) in a holographic printer; and usingsaid same holographic printer to produce a white light viewable hologramfrom said one or more intermediate holograms.
 51. A 2-step holographicprinter for printing an intermediate hologram (H3) using numerical dataobtained from a virtual or real camera, wherein camera brightness data^(kg)I_(ij) for one or more colour channels is obtained from aconstantly directed camera moving within a fixed rectangular cameraplane of the same size as a desired white light viewable hologram (H2)where i and j are respectively the x and y grid coordinates of aperspective view and k and g are respectively the x and y grid locationsof the camera position within said rectangular camera planecorresponding to said perspective view, wherein said camera brightnessdata is used to generate the data ^(μν)S_(αβ) displayed on a spatiallight modulator for each colour channel which is used to write thepixels of the intermediate hologram (H3) where μ and ν are respectivelythe x and y grid locations of a pixel on the spatial light modulator,such data being required for the writing of an H3 pixel whose x and ygrid locations are respectively α and β wherein:^(μν)S_(αβ)=^(kg)I_(ij) when 0<k≦N_(K) and 0<g≦N_(G) and 0<i≦N_(I) and0<j≦N_(J)=0 otherwise where $\begin{matrix}{k = {1 + {\left( {N_{K} - 1} \right)\left\lbrack {\frac{\left( {\alpha - 1} \right)\left( {1 + {2{a/h}}} \right)}{\left( {N_{A} - 1} \right)} + {2\frac{\left( {\mu - 1} \right)\left( {1 - {a/h}} \right)}{\left( {N_{M} - 1} \right)}} - 1} \right\rbrack}}} \\{i = {1 + \frac{\left( {N_{I} - 1} \right)\left( {\alpha - 1} \right)\left( {1 + {2{a/h}}} \right)}{\left( {N_{A} - 1} \right)} + \frac{\left( {N_{I} - 1} \right){a\left( {{a/h} - {2\left( {\mu - 1} \right)}} \right)}}{\left( {N_{M} - 1} \right)\left( {h - a} \right)}}} \\{j = {1 + \frac{\left( {N_{J} - 1} \right)\left( {\beta - 1} \right)\left( {1 + {2{a/h}}} \right)}{\left( {N_{B} - 1} \right)} + \frac{\left( {N_{J} - 1} \right){a\left( {{a/h} - {2\left( {v - 1} \right)}} \right)}}{\left( {N_{V} - 1} \right)\left( {h - a} \right)}}} \\{g = {1 + {\left( {N_{G} - 1} \right)\left\lbrack {\frac{\left( {\beta - 1} \right)\left( {1 + {2{a/h}}} \right)}{\left( {N_{B} - 1} \right)} + {2\frac{\left( {v - 1} \right)\left( {1 - {a/h}} \right)}{\left( {N_{V} - 1} \right)}} - 1} \right\rbrack}}}\end{matrix}$ where N values with majuscule subscript indices denote themaximum grid number for that certain index, a is the H2 to H3 distance,h is the H2 to H1 distance and all indices start counting at 1, andwherein the aspect ratio of the spatial light modulator is equal to theaspect ratio of the final white light viewable hologram (H2).
 52. A2-step holographic printer for printing an intermediate hologram (H3)using numerical data obtained from a virtual or real camera, whereincamera brightness data ^(kg)I_(ij) for one or more colour channels isobtained from a constantly directed camera moving within a fixedrectangular camera plane where i and j are respectively the x and y gridcoordinates of a perspective view and k and g are respectively the x andy grid locations of the camera position within said rectangular cameraplane corresponding to said perspective view, wherein said camerabrightness data is used to generate the data ^(μν)S_(αβ) displayed on aspatial light modulator for each colour channel which is used to writethe pixels of the intermediate hologram (H3) where μ and ν arerespectively the x and y grid locations of a pixel on the spatial lightmodulator, such data being required for the writing of an H3 pixel whosex and y grid locations are respectively α and β wherein^(μν)S_(αβ)=^(kg)I_(ij) when 0<k≦N_(K) and 0<g≦N_(G) and 0<i≦N_(I) and0<j≦N_(J)=0 otherwise where$k = {1 + {\left( {N_{K} - 1} \right)\left\{ {{\frac{1}{2}\left\lbrack {1 - \frac{D_{2}}{\Xi} - \frac{\Pi\quad h}{\left( {h - a} \right)\Xi}} \right\rbrack} + \frac{\left( {\alpha - 1} \right)\left( {D_{2} + \frac{a\quad\Pi}{h - a}} \right)}{\Xi\left( {N_{A} - 1} \right)} + \frac{\left( {\mu - 1} \right)\Pi}{\left( {N_{M} - 1} \right)\Xi}} \right\}}}$$i = {1 + {\left( {N_{I} - 1} \right)\left\{ {\frac{\left( {\alpha - 1} \right)\left( {1 + \frac{a\quad\Pi}{D_{2}\left( {h - a} \right)}} \right)}{\left( {N_{A} - 1} \right)} - \frac{a\quad{\Pi\left( {\mu - 1} \right)}}{{D_{2}\left( {h - a} \right)}\left( {N_{M} - 1} \right)}} \right\}}}$$g = {1 + {\left( {N_{G} - 1} \right)\left\{ {{\frac{1}{2}\left\lbrack {1 - \frac{R_{2}}{\Theta} - \frac{\Sigma\quad h}{\left( {h - a} \right)\Theta}} \right\rbrack} + \quad\frac{\left( {\beta - 1} \right)\left( {R_{2} + \frac{a\quad\Sigma}{h - a}} \right)}{\Theta\left( {N_{B} - 1} \right)} + \frac{\left( {v - 1} \right)\Sigma}{\left( {N_{V} - 1} \right)\Theta}} \right\}}}$$j = {1 + {\left( {N_{J} - 1} \right)\left\{ {\frac{\left( {\beta - 1} \right)\left( {1 + \frac{a\quad\Sigma}{R_{2}\left( {h - a} \right)}} \right)}{\left( {N_{B} - 1} \right)} - \frac{a\quad{\Sigma\left( {v - 1} \right)}}{{R_{2}\left( {h - a} \right)}\left( {N_{V} - 1} \right)}} \right\}}}$wherein N values with majuscule subscript indices denote the maximumgrid number for that certain index, a is the H2 to H3 distance, h is theH2 to H1 distance and all indices start counting at 1 and wherein D₂ isthe horizontal size of the H2 and R₂ is the vertical size of the H2 andwherein the H2 hologram viewing window is respectively of horizontal andvertical size Ξ and Θ and wherein π and Σ are respectively thehorizontal and vertical projected sizes of the spatial light modulatoron the viewing plane.
 53. A 2-step holographic printer as claimed inclaim 52, wherein said data ^(μν)S_(αβ) is corrected for opticaldistortions.
 54. A 2-step holographic printer as claimed in claim 52,wherein said data transformations for ^(μν)S_(αβ) are modified tocorrect for optical distortions.
 55. A holographic copying devicecomprising one or more pulsed laser sources, wherein said copying deviceis capable of generating an undistorted white light viewable hologram(H2) from one or more intermediate holograms (H3).
 56. A holographiccopying device as claimed in claim 55, wherein said one or moreintermediate holograms (H3) are written on a first substrate and saidwhite light viewable hologram (H2) is to be written on a secondsubstrate.
 57. A holographic copying device as claimed in claim 55,wherein said second substrate on which said white light viewablehologram (H2) is to be written is positioned parallel to said firstsubstrate.
 58. A holographic copying device as claimed in claim 57,wherein said second substrate is positioned at a distance d from saidfirst substrate wherein d is greater than zero and less than thedistance between the camera (H1) plane and the H2 plane.
 59. Aholographic copying device as claimed in claim 57, wherein said secondsubstrate is positioned at a distance d from said first substratewherein d is greater than zero and less than ¼ of the height of said oneor more intermediate holograms.
 60. A holographic copying device asclaimed in claim 57, wherein said second substrate is positioned at adistance d from said first substrate wherein d is greater than zero andless than ¼ of the width of said one or more intermediate holograms. 61.A 2-step holographic printer as claimed in claim 51, wherein said data^(μν)S_(αβ) is corrected for optical distortions.
 62. A 2-stepholographic printer as claimed in claim 51, wherein said datatransformations for ^(μν)S_(αβ) are modified to correct for opticaldistortions.